Ricercatore responsabile locale: FIRENZE ISTITUTO NAZIONALE DI FISICA NUCLEARE Preventivo per l'anno 2002 Struttura (a cura del rappresentante nazionale) Fisica Generale: misura di costanti fondamentali Dipartimento di Fisica e laboratorio LENS, Università di Firenze Misura della costante gravitazionale G mediante interferometria atomica Sviluppo di un gravimetro basato su interferometria atomica FIRENZE 4 anni Linea di ricerca Laboratorio ove si raccolgono i dati Acceleratore usato Fascio (sigla e caratteristiche) Processo fisico studiato Apparato strumentale utilizzato Sezioni partecipanti all'esperimento Istituzioni esterne all'Ente partecipanti Durata esperimento Mod. EN. 1 P R O G R A M M A D I R I C E R C A A) I N F O R M A Z I O N I G E N E R A L I B) S C A L A D E I T E M P I : piano di svolgimento PERIODO ATTIVITA’ PREVISTA 2002 -2003 2004 2005 Costruzione del sistema di vuoto e dell'apparato delle sorgenti laser (v. allegato). Realizzazione del gravimetro; acquisizione della massa sorgente (v. allegato). Misure preliminari; realizzazione del gradiometro (v. allegato). Ottimizzazione dell'apparato. Misura di G (v. allegato). Nuovo Esperimento Gruppo MAGIA 2 Guglielmo M. TINO Firenze Associato Guglielmo M. Tino [email protected]e-mail: Rappresentante Nazionale: Struttura di appartenenza: [email protected]e-mail: Posizione nell'I.N.F.N.:
Transcript
Ricercatoreresponsabile locale:
FIRENZE
ISTITUTO NAZIONALE DI FISICA NUCLEARE
Preventivo per l'anno 2002
Struttura
(a cura del rappresentante nazionale)
Fisica Generale: misura di costanti fondamentali
Dipartimento di Fisica e laboratorio LENS, Università di Firenze
Misura della costante gravitazionale G mediante interferometria atomica
Sviluppo di un gravimetro basato su interferometria atomica
FIRENZE
4 anni
Linea di ricerca
Laboratorio ovesi raccolgono i dati
Acceleratore usato
Fascio(sigla e caratteristiche)
Processo fisico studiato
Apparato strumentale utilizzato
Sezioni partecipanti all'esperimento
Istituzioni esterneall'Ente partecipanti
Durata esperimento
Mod. EN. 1
P R O G R A M M A D I R I C E R C A
A) I N F O R M A Z I O N I G E N E R A L I
B) S C A L A D E I T E M P I : piano di svolgimento
PERIODO ATTIVITA’ PREVISTA
2002 -2003
2004
2005
Costruzione del sistema di vuoto e dell'apparato delle sorgenti laser (v. allegato).
Realizzazione del gravimetro; acquisizione della massa sorgente (v. allegato).
Misure preliminari; realizzazione del gradiometro (v. allegato).
Ottimizzazione dell'apparato. Misura di G (v. allegato).
PROPOSERS' GROUPG.M. Tino Dipartimento di Fisica and European Lab. for Non-Linear SpectroscopyM. Inguscio Università di FirenzeC. Fort Largo E. Fermi, 2 - 50125 FIRENZEF. MinardiJ. StuhlerM. Fattori
INTERNATIONAL COLLABORATIONSA. Peters Universität Konstanz, GermanyM. Kasevich Yale University, USA
MAGIA: MISURA ACCURATA DI G MEDIANTE INTERFEROMETRIA ATOMICA
Research proposal submitted to INFN
P.I.: Guglielmo M. Tino,Dipartimento di Fisica e Laboratorio Europeo di Spettroscopia Nonlineare (LENS), Universitàdi Firenze
· PROPOSAL SUMMARY (ABSTRACT)
This proposal is for an experiment to measure the Newtonian gravitational constant G by a new
Esperimento GruppoMAGIA 2
ALLEGATO 1
MAGIA ALLEGATO 1 Pag.1Esperimento:
This proposal is for an experiment to measure the Newtonian gravitational constant G by a newmethod based on atom interferometry with ultracold atoms. Amongst the fundamental quantities,G is presently the one measured with the largest uncertainty and the different existingvalues disagree significantly.We propose to measure G by measuring the perturbation to the acceleration of free-fallingatoms due to a well-known source mass. Recently developed methods of atom interferometry withcold atoms should allow to increase the sensitivity by orders of magnitude with respect tostandard gravimeters. The use of atoms as simple test masses allows a better control oversystematic effects. The method could be extended in the future to the measurement of otherelusive physical quantities.
· PROJECT DESCRIPTION
The Newtonian gravitational constant G is, with the Planck's constant h and the speed oflight c, one of the most fundamental constants. While h is known with a relative uncertaintyof about 80 ppb and the value of c was measured to 9 decimal digits before being defined asexact, in the last adjustment of the fundamental quantities of physics the recommended valuefor the gravitational constant is G = (6.673 ± 0.010) x 10-11 m3kg-1s-2 [ ], corresponding toa relative uncertainty of ±1500 ppm. This is due to the weakness of gravity, to theimpossibility to shield it and to the difficulty of eliminating spurious forces.
Starting with the famous experiment performed by Cavendish in 1798, most measurements of Gwere performed using apparatus based on a torsion balance or pendulum. In spite of the largeimprovement in the experimental techniques, the reduction in the uncertainty in G has onlybeen of about two orders of magnitude in about 200 years and, still worse, measurements arein disagreement with each other in a significative way suggesting the presence ofuncontrolled systematic errors. For example, an anharmonicity was recently found in thesuspension of torsion balances.
We propose a new method to measure G by measuring the perturbation to the acceleration offree-falling atoms due to a well-known source mass. Recently developed methods of atominterferometry with cold atoms should allow to increase the sensitivity in the measurement ofthe acceleration by orders of magnitude with respect to standard gravimeters. The use ofatoms as simple test masses allows a better control over systematic effects.Matter-wave interference with neutral atoms was first demonstrated in 1991. In analogy tooptical interferometers, atomic wavepackets are split and recombined giving rise to aninterference signal. Different schemes can be used for splitting, reflecting and recombiningthe atoms and the atom optics components can be either material structures or light fields.In a particular class of interferometers, which is the one relevant for the present project,the separation of the atoms is achieved by inducing a transition between internal states ofthe atoms by an electromagnetic field. The spatial separation in this case is induced by themomentum recoil and the internal and external states of the atoms become entangled. The fieldis now mature both from the point of view of the understanding of the basic physicsunderlying laser cooling and laser manipulation of atoms and for the development of a solidtechnology for the experimental implementation of sensors. Atom interferometers are alreadycompeting with state-of-the-art optical interferometers in terms of sensitivity in themeasurement, for example, of gravity acceleration and rotations [ , ].
Already in 1975, a neutron interferometer was used to detect the phase shift caused by theEarth's gravitational field. The inertial sensitivity of an atom interferometer can be muchlarger than the one of neutron interferometers because of the larger mass and theavailability of sources of slow atoms. Indeed, the sensitivity of atom interferometers asdetectors of rotations and accelerations increases with the observation time so that it canbe extremely high if slow laser-cooled atoms are used. Laser cooling of atoms has been one ofthe most active fields of research in physics in the last decade. Atoms from aroom-temperature vapour can be cooled to temperatures as low as a few microkelvin byinteracting with laser light. At such low temperatures, the wave properties of the atomsbecome relevant and the corresponding de Broglie wavelength can be comparable to the distancebetween the atoms. This gives rise to completely new phenomena such as Bose-Einsteincondensation and allows to perform experiment where the matter waves interfere just as usualwaves do. In 1997, the Nobel prize in Physics was awarded to C. Cohen-Tannoudji, S. Chu andW.D. Phillips for their contribution in this field. Proposing groups of this project havebeen active in this field for about ten years. At LENS and Department of Physics in Florencethere are at present 3 different cold atoms apparatus running.
An experiment conceptually similar to the one we propose was reported in [ ]. The position ofa macroscopic free-falling body was tracked by a laser interferometer and the perturbation to
MAGIA ALLEGATO 1 Pag.2Esperimento:
a macroscopic free-falling body was tracked by a laser interferometer and the perturbation toits acceleration induced by a source mass was measured. We believe that our idea of usingatoms instead of macroscopic bodies as proof masses will provide important advantages interms of achievable sensitivity and final accuracy. The use of atomic proof masses insuresreproducibility in different experiments and allows for accurate characterization ofenvironmental perturbations. For example, the effect of magnetic and electric fields can bedirectly measured from atomic properties. In addition, the acceleration of the atoms can bemeasured with an extremely high accuracy by atom interferometry using methods that arebasically related to atomic clocks. Other more specific and technical aspects that will leadto significative improvements with respect to previous experiments will be discussed in thetechnical section of this proposal.
MAGIA will allow the proposing group to develop an apparatus with an extremely highsensitivity for the measurement of gravity acceleration and to perform an accuratemeasurement of the Newtonian constant G. We will evaluate different experimental strategiesbefore choosing the actual scheme including the use of a Bose-Einstein condensate and thecombination of two gravimeters to form a gradiometer. From the experimental point of view,all these methods, although rather sophisticated, are well within the possibilities of theproposing group.
The apparatus we will develop could be extended in the future to the measurement of otherelusive physical quantities. Examples of such future experiments to be considered aremeasurements of the field curvature, search for a deviation from the 1/r2 law, tests of theweak equivalence principle (with the possibility of comparing bosonic with fermionic atoms)and, in general, the detection of effects where high sensitivity interferometric detection isrequired. If gravity is measured independently, such an apparatus can provide an accuratemeasurement of the ratio h/m of Planck's constant to the atomic mass which appears in theexpression of the fine structure constant.
It is worth mentioning here that accurate inertial sensors have also important applicationsincluding navigation, location of natural resources, prediction of earthquakes and volcaniceruptions.
In conclusion, the main objectives and outcomes of the MAGIA project are the following:
1) Development of an accurate gravimeter based on interferometry with ultracold Rb atoms.
2) Investigation of the possibility of using Bose-Einstein condensed atoms and twogravimeters to increase sensitivity and accuracy.
3) Determination of the Newtonian gravitational constant G.
· TECHNICAL APPROACH
- Atom interferometer
In an atom interferometer, atomic wavepackets are split and then recombined giving rise to aninterference signal when atoms are detected. Different schemes can be used for splitting,reflecting and recombining the atoms and the atom optics components can be either materialstructures or light fields. In a particular class of interferometers, which is the onerelevant for the present project, the separation of the atoms is achieved by inducing a Ramantransition between internal states of the atoms by an electromagnetic field. The spatialseparation in this case is induced by the momentum recoil and the internal and externalstates of the atoms become entangled.
We plan to develop an atom interferometer based on a fountain of laser-cooled rubidium atoms.The basic scheme of the apparatus is similar to the gravimeter (shown in the figure) recentlydemonstrated by the group of S. Chu at Stanford with Cs atoms [2]. In our experiment,however, we plan to use Rb atoms and to improve the gravimeter performance in several pointsin view of an accurate determination of G.
Atoms collected from the background vapor using laser cooling and trapping methods arelaunched upward with a well controlled velocity. Initially the atoms are pumped in one of thehyperfine states of the atom ground state. During the flight, optical pulses are used tostimulate Raman transitions between two different hyperfine states. In the transition, a
MAGIA ALLEGATO 1 Pag.3Esperimento:
stimulate Raman transitions between two different hyperfine states. In the transition, amomentum hk is transferred to the atom. Assuming that the atoms is initially in the internalstate |1> with a momentum p, the sequence is schematically the following:1) a first pulse (p/2 pulse) puts an atom into a superposition of the initial state |1,p> andthe second state |2,p+hk> which separate spatially. As an atom optics component, thiscorresponds to a beam splitter.2) After a time T, a second pulse (p pulse) induces the transitions |1,p> ® |2,p+hk> and|2,p+hk> ® |1,p> for the two parts of the atoms. This corresponds to the mirrors in anoptical interferometer.3) After another time T, the two parts of the atoms overlap again and a third pulse (p/2pulse) acts as a recombining beam splitter.At the end of the pulse sequence the number of atoms in either of the states is detected. Fora proper arrangement of experimental parameters, it can be shown that the phase differencebetween the two arms of the interferometer is DF = kgT2. The sensitivity of the methodtherefore increases with the interrogation time and this is the reason to use an atomicfountain scheme. The expression also shows that an increase in sensitivity can be obtained ifa shorter wavelength is used to induce the Raman transition. In the same way, a significativeincrease of the sensitivity can be achieved if each pulse of the sequence is replaced by asequence of pulses, thus increasing the spatial separation between the two parts of theatomic wavepacket.The Raman transition between two internal states can be induced using two laser beams whosefrequency difference is phase-locked to a stable microwave source. This insures a precisecontrol of the relative phase. Frequency stability can be obtained using lasers locked toatomic resonances.
A crucial element of the interferometer is the mirror used to retroreflect the Raman laserbeams. This mirror plays the role of an inertial reference during the measurement. Indeed thetwo laser beams can be arranged to travel along the same path and only vibrations of thismirror can affect the relative phase. Therefore this mirror will be stabilized using activelow-frequency vibration isolation systems to reduce vibrations in the 0.1-10 Hz range. Thebetter the mirror vibration isolation, the larger can be the time T between pulses and theresulting sensitivity.
An important advantage of the proposed experimental scheme is that it is free of instrumentaldrifts thus allowing integration over very long time intervals to increase sensitivity. Inorder to compensate for environmental changes during the experiment, we plan to use a highsensitivity gravimeter as a reference.
- Source mass
As discussed above, the basic idea of the experiment we propose is to measure theperturbation to the acceleration of free-falling atoms due to a well-known source mass. Fromthe knowledge of the mass and shape of the body used as source mass, the gravitationalconstant can be extracted.The choice of the shape, size and the material to be used will be the subject of the initialstudy phase of the experiment. A high density material must be used; it is also important,however, to choose a material that can be easily machined and can guarantee a gooduniformity. Based on a preliminary estimate, we plan to use a tungsten torus with a mass of500-1000 kg. The choice will also depend on the project budget.As in most previous experiments to determine G, we will perform a differential measurement:The source mass will be placed alternatively above and below the measurement region producinga decrease or an increase of the atoms acceleration. The differential measurement will allowus to drastically reduce common mode errors.
- Gradiometer
We will study the possibility of combining two similar gravimeters toa gradiometer. An atom interferometer-based gravity gradiometer was already demonstrated in []. Such a configuration would certainly increase the complexity of the setup but not as muchas doubling the apparatus. Much of the setup would be common to the two gravimeters, namely,the laser sources and most of the optical setup. The gradiometer would likely lead to asignificant increase in sensitivity. The expected advantages of this scheme in themeasurement of G would be a reduction of the sensitivity to vibrations and to other sourcesof noise, that would cancel in the difference, and an increase of the signal. In this case,indeed, we would measure the variation in the difference of the accelerations of the twosamples of atoms as a function of the source mass position, that would double the signal and
MAGIA ALLEGATO 1 Pag.4Esperimento:
samples of atoms as a function of the source mass position, that would double the signal andreduce the effect of common mode noise.
- BEC
This project is based on the experimental scheme described above. During the development ofthe project, however, we will investigate possible alternative schemes. This study willlikely lead to improvements of the apparatus in the course of this project or will allow toplan for future experiments with improved apparatus.An important possibility we will investigate is to use atoms from a Bose-Einstein condensateinstead of the "thermal" atoms produced by laser cooling. This possibility has not beendeeply investigated yet since Bose-Einstein condensation has only been observed in 1995 forthe first time. At LENS and Department of Physics in Firenze, a BEC apparatus is operatingsince 1999 [ ] and two more are being completed. Similar to the light emitted by a laser,atoms extracted from a Bose-Einstein condensate show a high degree of coherence that can inprinciple improve the interferometer performance. The improvement could be not only a simpleincrease in sensitivity but completely different schemes could be devised based on thespecific properties of this atom source. We will investigate in particular possible schemesfor "local" measurements of gravity that would not require the correction for the Earth'sfield gradient which is necessary in the apparatus based on free-falling atoms.The advantages which can be expected from the use of a Bose-Einstein condensate will have tobe compared with limitations due to a smaller number of atoms, a higher complexity of theapparatus and possible spurious effects due, for example, to the presence of the magnetictrap.
- Existing apparatus
As already mentioned, at LENS and Department of Physics in Florence there are at present 3different cold atoms apparatus running. One of these has been designed with a verticalstructure in order to produce a "fountain" of ultracold Rb atoms. It will form the basis ofthe apparatus to be developed in the frame of this project. The present apparatus is based ona double-magneto-optical scheme that allows a fast collection of the Rb atoms from the vapourin a first cell while keeping a very low background pressure in the cell where experimentsare performed [ ]. More than 109 atoms can be trapped in less than one second and the traplifetime is several tens of seconds. A magnetic trap has been mounted in the apparatus thatwould allow efficient magnetic trapping and evaporative cooling of the atoms down toBose-Einstein condensation.For the experiment proposed in this project, the existing apparatus will need significativechanges due to the stringent requirements to achieve the planned levels of sensitivity andaccuracy. Main changes concern accurate magnetic shielding of the interaction region,development of an active vibration isolation system for critical optics in theinterferometer, phase-locking of diode lasers, light amplification using tapered amplifiers,and development of optics and electronics needed to induce Raman transitions with therequired spatial uniformity and phase stability of the laser light. As discussed above, partsof the apparatus, including vacuum, optics and electronics parts, will have to be doubled torealize an atomic gradiometer.
- Expected accuracy
The sensitivity of the apparatus can be estimated using the expression for the phase changegiven above: DF = kgT2. If we consider Rb atoms excited by Raman transition using light witha wavelength corresponding to the D2 line (l = 780 nm) and T = 200 ms, a change of 2p in thephase between the two arms of the interferometer corresponds to 10-6 g. A sensitivity Dg/g"10-10-10-11 range can then be achieved because of the intrinsic stability of the apparatusthat allows long integration time. In fact, the accuracy of the apparatus is generally not ashigh as its sensitivity. However, because we plan to perform a differential measurement, or adouble differential measurement if a gradiometer is used, possible systematic errors will notaffect the measurement of G. The maximum sensitivity can then be assumed as the relevantfigure for this experiment.The accuracy in the determination of G obviously depends on the size of the accelerationchange induced by the source mass. If we assume to use a tungsten mass with the shape of atorus similar to the one used in [4], the resulting variation in the acceleration is of theorder of 10-7 g. From the estimated sensitivity of the apparatus, a relative uncertainty of10-3-10-4 in the determination of G results. In fact, we believe that the small size of theapparatus will allow us to optimize the shape and the resulting effect of the source mass. In
PROPOSERS’ GROUPG.M. Tino Dipartimento di Fisica and European Lab. for Non-Linear SpectroscopyM. Inguscio Università di FirenzeC. Fort Largo E. Fermi, 2 – 50125 FIRENZEF. MinardiJ. StuhlerM. Fattori
INTERNATIONAL COLLABORATIONSA. Peters Universität Konstanz, GermanyM. Kasevich Yale University, USA
P.I.: Guglielmo M. Tino,Dipartimento di Fisica e Laboratorio Europeo di Spettroscopia Nonlineare (LENS), Università di Firenze
• PROPOSAL SUMMARY (ABSTRACT)
This proposal is for an experiment to measure the Newtonian gravitational constant G by a newmethod based on atom interferometry with ultracold atoms. Amongst the fundamental quantities, Gis presently the one measured with the largest uncertainty and the different existing values disagreesignificantly.
We propose to measure G by measuring the perturbation to the acceleration of free-fallingatoms due to a well-known source mass. Recently developed methods of atom interferometry withcold atoms should allow to increase the sensitivity by orders of magnitude with respect to standardgravimeters. The use of atoms as simple test masses allows a better control over systematic effects.The method could be extended in the future to the measurement of other elusive physical quantities.
• PROJECT DESCRIPTION
The Newtonian gravitational constant G is, with the Planck’s constant h and the speed of lightc, one of the most fundamental constants. While h is known with a relative uncertainty of about 80ppb and the value of c was measured to 9 decimal digits before being defined as exact, in the lastadjustment of the fundamental quantities of physics the recommended value for the gravitationalconstant is G = (6.673 ± 0.010) x 10-11 m3kg-1s-2 [1], corresponding to a relative uncertainty of±1500 ppm. This is due to the weakness of gravity, to the impossibility to shield it and to thedifficulty of eliminating spurious forces.
Starting with the famous experiment performed by Cavendish in 1798, most measurements ofG were performed using apparatus based on a torsion balance or pendulum. In spite of the largeimprovement in the experimental techniques, the reduction in the uncertainty in G has only been ofabout two orders of magnitude in about 200 years and, still worse, measurements are indisagreement with each other in a significative way suggesting the presence of uncontrolledsystematic errors. For example, an anharmonicity was recently found in the suspension of torsionbalances.
We propose a new method to measure G by measuring the perturbation to the acceleration offree-falling atoms due to a well-known source mass. Recently developed methods of atominterferometry with cold atoms should allow to increase the sensitivity in the measurement of theacceleration by orders of magnitude with respect to standard gravimeters. The use of atoms assimple test masses allows a better control over systematic effects.
MAGIA
3
Matter-wave interference with neutral atoms was first demonstrated in 1991. In analogy tooptical interferometers, atomic wavepackets are split and recombined giving rise to an interferencesignal. Different schemes can be used for splitting, reflecting and recombining the atoms and theatom optics components can be either material structures or light fields. In a particular class ofinterferometers, which is the one relevant for the present project, the separation of the atoms isachieved by inducing a transition between internal states of the atoms by an electromagnetic field.The spatial separation in this case is induced by the momentum recoil and the internal and externalstates of the atoms become entangled. The field is now mature both from the point of view of theunderstanding of the basic physics underlying laser cooling and laser manipulation of atoms and forthe development of a solid technology for the experimental implementation of sensors. Atominterferometers are already competing with state-of-the-art optical interferometers in terms ofsensitivity in the measurement, for example, of gravity acceleration and rotations [2,3].
Already in 1975, a neutron interferometer was used to detect the phase shift caused by theEarth’s gravitational field. The inertial sensitivity of an atom interferometer can be much larger thanthe one of neutron interferometers because of the larger mass and the availability of sources of slowatoms. Indeed, the sensitivity of atom interferometers as detectors of rotations and accelerationsincreases with the observation time so that it can be extremely high if slow laser-cooled atoms areused. Laser cooling of atoms has been one of the most active fields of research in physics in the lastdecade. Atoms from a room-temperature vapour can be cooled to temperatures as low as a fewmicrokelvin by interacting with laser light. At such low temperatures, the wave properties of theatoms become relevant and the corresponding de Broglie wavelength can be comparable to thedistance between the atoms. This gives rise to completely new phenomena such as Bose-Einsteincondensation and allows to perform experiment where the matter waves interfere just as usualwaves do. In 1997, the Nobel prize in Physics was awarded to C. Cohen-Tannoudji, S. Chu andW.D. Phillips for their contribution in this field. Proposing groups of this project have been activein this field for about ten years. At LENS and Department of Physics in Florence there are atpresent 3 different cold atoms apparatus running.
An experiment conceptually similar to the one we propose was reported in [4]. The position ofa macroscopic free-falling body was tracked by a laser interferometer and the perturbation to itsacceleration induced by a source mass was measured. We believe that our idea of using atomsinstead of macroscopic bodies as proof masses will provide important advantages in terms ofachievable sensitivity and final accuracy. The use of atomic proof masses insures reproducibility indifferent experiments and allows for accurate characterization of environmental perturbations. Forexample, the effect of magnetic and electric fields can be directly measured from atomic properties.In addition, the acceleration of the atoms can be measured with an extremely high accuracy by atominterferometry using methods that are basically related to atomic clocks. Other more specific andtechnical aspects that will lead to significative improvements with respect to previous experimentswill be discussed in the technical section of this proposal.
MAGIA will allow the proposing group to develop an apparatus with an extremely highsensitivity for the measurement of gravity acceleration and to perform an accurate measurement ofthe Newtonian constant G. We will evaluate different experimental strategies before choosing theactual scheme including the use of a Bose-Einstein condensate and the combination of twogravimeters to form a gradiometer. From the experimental point of view, all these methods,although rather sophisticated, are well within the possibilities of the proposing group.
The apparatus we will develop could be extended in the future to the measurement of otherelusive physical quantities. Examples of such future experiments to be considered are
MAGIA
4
measurements of the field curvature, search for a deviation from the 1/r2 law, tests of the weakequivalence principle (with the possibility of comparing bosonic with fermionic atoms) and, ingeneral, the detection of effects where high sensitivity interferometric detection is required. Ifgravity is measured independently, such an apparatus can provide an accurate measurement of theratio h/m of Planck’s constant to the atomic mass which appears in the expression of the finestructure constant.
It is worth mentioning here that accurate inertial sensors have also important applicationsincluding navigation, location of natural resources, prediction of earthquakes and volcaniceruptions.
In conclusion, the main objectives and outcomes of the MAGIA project are the following:
1) Development of an accurate gravimeter based on interferometry with ultracold Rb atoms.
2) Investigation of the possibility of using Bose-Einstein condensed atoms and two gravimeters toincrease sensitivity and accuracy.
3) Determination of the Newtonian gravitational constant G.
• TECHNICAL APPROACH
- Atom interferometer
In an atom interferometer, atomic wavepackets are split andthen recombined giving rise to an interference signal whenatoms are detected. Different schemes can be used for splitting,reflecting and recombining the atoms and the atom opticscomponents can be either material structures or light fields. In aparticular class of interferometers, which is the one relevant forthe present project, the separation of the atoms is achieved byinducing a Raman transition between internal states of the atomsby an electromagnetic field. The spatial separation in this case isinduced by the momentum recoil and the internal and externalstates of the atoms become entangled.
We plan to develop an atom interferometer based on afountain of laser-cooled rubidium atoms. The basic scheme ofthe apparatus is similar to the gravimeter (shown in the figure)recently demonstrated by the group of S. Chu at Stanford withCs atoms [2]. In our experiment, however, we plan to use Rbatoms and to improve the gravimeter performance in severalpoints in view of an accurate determination of G.
Atoms collected from the background vapor using laser cooling and trapping methods arelaunched upward with a well controlled velocity. Initially the atoms are pumped in one of thehyperfine states of the atom ground state. During the flight, optical pulses are used to stimulate
MAGIA
5
Raman transitions between two different hyperfine states. In the transition, a momentum hk istransferred to the atom. Assuming that the atoms is initially in the internal state |1> with amomentum p, the sequence is schematically the following:1) a first pulse (π/2 pulse) puts an atom into a superposition of the initial state |1,p> and the secondstate |2,p+hk> which separate spatially. As an atom optics component, this corresponds to a beamsplitter.2) After a time T, a second pulse (π pulse) induces the transitions |1,p> → |2,p+hk> and |2,p+hk>→ |1,p> for the two parts of the atoms. This corresponds to the mirrors in an optical interferometer.3) After another time T, the two parts of the atoms overlap again and a third pulse (π/2 pulse) actsas a recombining beam splitter.
At the end of the pulse sequence the number of atoms in either of the states is detected. For aproper arrangement of experimental parameters, it can be shown that the phase difference betweenthe two arms of the interferometer is ∆Φ = kgT2. The sensitivity of the method therefore increaseswith the interrogation time and this is the reason to use an atomic fountain scheme. The expressionalso shows that an increase in sensitivity can be obtained if a shorter wavelength is used to inducethe Raman transition. In the same way, a significative increase of the sensitivity can be achieved ifeach pulse of the sequence is replaced by a sequence of pulses, thus increasing the spatial separationbetween the two parts of the atomic wavepacket.
The Raman transition between two internal states can be induced using two laser beams whosefrequency difference is phase-locked to a stable microwave source. This insures a precise control ofthe relative phase. Frequency stability can be obtained using lasers locked to atomic resonances.
A crucial element of the interferometer is the mirror used to retroreflect the Raman laser beams.This mirror plays the role of an inertial reference during the measurement. Indeed the two laserbeams can be arranged to travel along the same path and only vibrations of this mirror can affect therelative phase. Therefore this mirror will be stabilized using active low-frequency vibrationisolation systems to reduce vibrations in the 0.1-10 Hz range. The better the mirror vibrationisolation, the larger can be the time T between pulses and the resulting sensitivity.
An important advantage of the proposed experimental scheme is that it is free of instrumentaldrifts thus allowing integration over very long time intervals to increase sensitivity. In order tocompensate for environmental changes during the experiment, we plan to use a high sensitivitygravimeter as a reference.
- Source mass
As discussed above, the basic idea of the experiment we propose is to measure the perturbationto the acceleration of free-falling atoms due to a well-known source mass. From the knowledge ofthe mass and shape of the body used as source mass, the gravitational constant can be extracted.
The choice of the shape, size and the material to be used will be the subject of the initial studyphase of the experiment. A high density material must be used; it is also important, however, tochoose a material that can be easily machined and can guarantee a good uniformity. Based on apreliminary estimate, we plan to use a tungsten torus with a mass of 500-1000 kg. The choice willalso depend on the project budget.
As in most previous experiments to determine G, we will perform a differential measurement:The source mass will be placed alternatively above and below the measurement region producing adecrease or an increase of the atoms acceleration. The differential measurement will allow us todrastically reduce common mode errors.
MAGIA
6
- Gradiometer
We will study the possibility of combining two similar gravimeters to form a gradiometer. Anatom interferometer-based gravity gradiometer was already demonstrated in [5]. Such aconfiguration would certainly increase the complexity of the setup but not as much as doubling theapparatus. Much of the setup would be common to the two gravimeters, namely, the laser sourcesand most of the optical setup. The gradiometer would likely lead to a significant increase insensitivity. The expected advantages of this scheme in the measurement of G would be a reductionof the sensitivity to vibrations and to other sources of noise, that would cancel in the difference, andan increase of the signal. In this case, indeed, we would measure the variation in the difference ofthe accelerations of the two samples of atoms as a function of the source mass position, that woulddouble the signal and reduce the effect of common mode noise.
- BEC
This project is based on the experimental scheme described above. During the development ofthe project, however, we will investigate possible alternative schemes. This study will likely lead toimprovements of the apparatus in the course of this project or will allow to plan for futureexperiments with improved apparatus.
An important possibility we will investigate is to use atoms from a Bose-Einstein condensateinstead of the “thermal” atoms produced by laser cooling. This possibility has not been deeplyinvestigated yet since Bose-Einstein condensation has only been observed in 1995 for the first time.At LENS and Department of Physics in Firenze, a BEC apparatus is operating since 1999 [6] andtwo more are being completed. Similar to the light emitted by a laser, atoms extracted from a Bose-Einstein condensate show a high degree of coherence that can in principle improve theinterferometer performance. The improvement could be not only a simple increase in sensitivity butcompletely different schemes could be devised based on the specific properties of this atom source.We will investigate in particular possible schemes for “local” measurements of gravity that wouldnot require the correction for the Earth’s field gradient which is necessary in the apparatus based onfree-falling atoms.
The advantages which can be expected from the use of a Bose-Einstein condensate will have tobe compared with limitations due to a smaller number of atoms, a higher complexity of theapparatus and possible spurious effects due, for example, to the presence of the magnetic trap.
- Existing apparatus
As already mentioned, at LENS and Department of Physics in Florence there are at present 3different cold atoms apparatus running. One of these has been designed with a vertical structure inorder to produce a “fountain” of ultracold Rb atoms. It will form the basis of the apparatus to bedeveloped in the frame of this project. The present apparatus is based on a double-magneto-opticalscheme that allows a fast collection of the Rb atoms from the vapour in a first cell while keeping avery low background pressure in the cell where experiments are performed [7]. More than 109
atoms can be trapped in less than one second and the trap lifetime is several tens of seconds. Amagnetic trap has been mounted in the apparatus that would allow efficient magnetic trapping andevaporative cooling of the atoms down to Bose-Einstein condensation.
For the experiment proposed in this project, the existing apparatus will need significativechanges due to the stringent requirements to achieve the planned levels of sensitivity and accuracy.
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Main changes concern accurate magnetic shielding of the interaction region, development of anactive vibration isolation system for critical optics in the interferometer, phase-locking of diodelasers, light amplification using tapered amplifiers, and development of optics and electronicsneeded to induce Raman transitions with the required spatial uniformity and phase stability of thelaser light. As discussed above, parts of the apparatus, including vacuum, optics and electronicsparts, will have to be doubled to realize an atomic gradiometer.
- Expected accuracy
The sensitivity of the apparatus can be estimated using the expression for the phase changegiven above: ∆Φ = kgT2. If we consider Rb atoms excited by Raman transition using light with awavelength corresponding to the D2 line (λ = 780 nm) and T = 200 ms, a change of 2π in the phasebetween the two arms of the interferometer corresponds to 10-6 g. A sensitivity ∆g/g ≈10-10-10-11
range can then be achieved because of the intrinsic stability of the apparatus that allows longintegration time. In fact, the accuracy of the apparatus is generally not as high as its sensitivity.However, because we plan to perform a differential measurement, or a double differentialmeasurement if a gradiometer is used, possible systematic errors will not affect the measurement ofG. The maximum sensitivity can then be assumed as the relevant figure for this experiment.
The accuracy in the determination of G obviously depends on the size of the accelerationchange induced by the source mass. If we assume to use a tungsten mass with the shape of a torussimilar to the one used in [4], the resulting variation in the acceleration is of the order of 10-7 g.From the estimated sensitivity of the apparatus, a relative uncertainty of 10-3-10-4 in thedetermination of G results. In fact, we believe that the small size of the apparatus will allow us tooptimize the shape and the resulting effect of the source mass. In addition, several aspects of theapparatus can be optimized to increase the sensitivity significantly. Therefore we expect to achievean accuracy in the determination of G better than 100 ppm. It is worth emphasizing that this wouldrepresent not only an improvement by more than one order of magnitude with respect to thepresently accepted value but it would be obtained with a method completely different from previousexperiments. Considering the large discrepancy between the values obtained so far, this resultwould be important to discriminate amongst them.
• REFERENCES 1. P.J. Mohr, B.N. Taylor, Rev. Mod. Phys. 72, 351 (2000) and references therein.2. A. Peters, K.Y.Chung, S.Chu, Nature 400, 849 (1999).3. T.L. Gustavson, A. Landragin, M. Kasevich, Class. Quantum Grav. 17, 2385 (2000).4. J.P. Schwarz, D.S. Robertson, T.M. Niebauer, J.E. Faller, Science 282, 2230 (1998).5. M.J. Snadden, J.M. McGuirk, P. Bouyer, K.G. Haritos, M.A. Kasevich, Phys. Rev. Lett. 81, 971(1998).6. C. Fort, M. Prevedelli, F. Minardi, F.S. Cataliotti, L. Ricci, G.M. Tino, M. Inguscio, Europhys.Lett. 49, 8 (2000).7. L. Cacciapuoti, A. Castrillo, M. de Angelis, G.M. Tino, Eur. Phys. J. D, in press.
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• WORK PLAN
We propose a 4 years development program involving LENS and in collaboration with thegroup of M. Kasevich at Yale.
At the end of the program, the expected results is an accurate determination of the value of Gwith a method which is qualitatively different from the ones used so far.
The main tasks of the MAGIA project are listed in Table 1. The planned performance periodsare indicated in Table 2. Dates for the achievement of listed tasks are based on January 2002effective start date.
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Table 1. MAGIA project main tasks
Main Tasks Description Date ofachievement
T.1 Construction of vacuum and laser system for the cold-atoms interferometer 12/2002
T.2 Construction of phase-locked, amplified laser system 12/2002
Guglielmo M. Tino (Project PI)Guglielmo M. Tino got his PhD in Physics from the Scuola Normale Superiore di Pisa in 1992. He has been Professorof Physics of Matter at the University of Napoli since 1998. Starting November 2001 he will be at the University ofFirenze. Tino is associated to LENS. He published about 70 scientific papers. His main research interests are highprecision spectroscopy, experimental tests of fundamental laws, laser cooling and trapping of atoms, and atominterferometry. He organized, with Prof. R.C. Hilborn from Amherst College, the international conference on "Spin-statistics connection and commutation relations: Experimental tests and theoretical implications", Anacapri, 31/5-3/6,2000 and was the co-editor of the proceedings volume published by American Institute of Physics. Tino was the scientific manager of different projects:- Progetto nazionale dell'Agenzia Spaziale Italiana (ASI '91-'95) su "Intrappolamento di atomi con radiazione laser incondizioni di microgravità" (Responsabile Nazionale).- Progetto di ricerca scientifica e tecnologica del MURST (40%-1996) su "Fisica atomica per la metrologia"(Responsabile Unità Operativa).- Programma di ricerca scientifica di rilevante interesse nazionale (PRIN-1998) su "Interazioni non lineari tra impulsilaser ultracorti ed atomi", (Responsabile scientifico dell'Unità di Ricerca).- Progetto avanzato di Sezione dell'INFM (PAIS99) su "Optical manipulation of ultracold atoms" (ResponsabileNazionale).- Intervento speciale di Sezione dell'INFM (PAIS2000) su "Optical confinement of Bose-Einstein condensates" (Projectmanager).
Selected publications of G.M. Tino:
- G.M. Tino, L. Hollberg, A. Sasso, M. Barsanti, M. Inguscio:"Hyperfine structure of the metastable 5S2 state of 17Ousing an AlGaAs diode laser at 777 nm", Phys. Rev. Lett. 64 , 2999 (1990). - G.M.Tino, M.Barsanti, M.de Angelis, L.Gianfrani, M.Inguscio: "Spectroscopy of the 689 nm intercombination lineof strontium using an extended-cavity InGaP/InGaAlP diode laser", Appl. Phys. B 55, 397 (1992).- F.S. Pavone, G. Giusfredi, A. Capanni, M. Inguscio, M. de Angelis, G.M.Tino: "Narrow-linewidth visible diodelaser at 690 nm. Spectroscopy of the SrI inter-combination line", in Frequency Stabilized Lasers and TheirApplications, Y.C. Chung ed., SPIE vol.1837, pag. 366 (1992).- C. Albanese, R. Fortezza, M. Inguscio, G.M. Tino: "Laser cooling and trapping of atoms in microgravity: ultracoldatoms collisions", in Materials and Fluid Sciences in Microgravity, ESA SP-333, pag. 869 (1992).- G. Santarelli, A. Clairon, S.N. Lea, G.M. Tino: "Heterodyne optical phase-locking of extended-cavity diode lasers at9 GHz", Opt. Commun. 104, 339 (1994).- A.S. Zibrov, R.W. Fox, R. Ellingsen, C.S. Weimer, V.L. Velichansky, G.M. Tino, L.Hollberg: "High-resolutiondiode laser spectroscopy of calcium", Appl. Phys. B 59, 327 (1994).- J. Reichel, O. Morice, G.M. Tino, C. Salomon: "Subrecoil Raman cooling of cesium atoms", Europhys. Lett. 28, 477(1994).- C. Fort, F. Cataliotti, P. Raspollini, G.M. Tino, M. Inguscio: "Optical double-resonance spectroscopy of trapped Csatoms: hyperfine structure of the 8s and 6d excited states", Z. Phys. D 34, 91 (1995).- M. de Angelis, G. Gagliardi, L. Gianfrani, G.M. Tino: "Test of the symmetrization postulate for spin-0 particles",Phys. Rev. Lett. 76, 2840 (1996).- B. Preziosi, G.M. Tino: "Possible tests of curvature effects in weak gravitational fields", Gen. Relat. Gravit. 30, 173(1998).- F.S. Cataliotti, E.A. Cornell, C. Fort, M. Inguscio, F. Marin, M. Prevedelli, L. Ricci, G.M. Tino:"Magneto-opticaltrapping of Fermionic potassium atoms",Phys. Rev. A 57, 1136 (1998).- G. Modugno, M. Inguscio, G.M. Tino:"Search for small violations of the symmetrization postulate for spin-0particles", Phys. Rev. Lett. 81, 4790 (1998).- M. Prevedelli, F.S. Cataliotti, E.A. Cornell, J.R. Ensher, C. Fort, L. Ricci, G.M. Tino, M. Inguscio:"Trapping andcooling of potassium isotopes in a double-magneto-optical-trap apparatus", Phys. Rev. A 59, 886 (1999).- G.M. Tino, F.S. Cataliotti, E.A. Cornell, C. Fort, M. Inguscio, M. Prevedelli:"Towards quantum degeneracy ofbosonic and fermionic potassium atoms", in Bose-Einstein condensation in atomic gases, Proceedings of theInternational School of Physics "E. Fermi", Course CXL, M. Inguscio, S. Stringari and C. Wieman (Eds.), p. 521, IOSPress, Amsterdam (1999).- C. Fort, M. Prevedelli, F. Minardi, F.S. Cataliotti, L. Ricci, G.M. Tino, M. Inguscio:"Collective excitations of a 87RbBose condensate in the Thomas-Fermi regime", Europhys. Lett. 49, 8 (2000).
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Massimo InguscioMassimo Inguscio got his PhD in Physics from the Scuola Normale Superiore di Pisa in 1978. He is presently Professorof Physics of Matter at the University of Firenze. He published about 150 scientific papers and has been the editor ofabout 10 books including proceedings of international physics conferences and schools as, for example, theInternational Conference of Laser Spectroscopy (World Scientific,1996) and International Conference of AtomicPhysics (AIP,2000). Since 1998, Inguscio is the Director of the European Laboratory for Nonlinear Spectroscopy-LENS in Firenze.His research activity focused on the interaction of laser light with atoms and molecules with new laser sources andmethods for high precision spectroscopy. In the last years, his main research interests have concerned the accuratemeasurement of fundamental constants, the investigation of phenomena involving the interaction of cold atoms withcoherent light and the physics of Bose-Einstein condensation in atomic vapors.
Marco Fattori2000: Laurea degree cum laude from University of Firenze;2001- : PhD student in Physics, University of Firenze.
Chiara Fort1992: Laurea degree cum laude from University of Firenze;1996: PhD degree in Physics, University of Firenze;1997- : Research position, permanent, LENS
Francesco Minardi1988-1992: Scuola Normale Superiore, Pisa;17 July 1993: Laurea degree cum laude from University of Pisa;24 April 1998: PhD degree in Physics, University of Pisa1998-1999: Post-doc appointments at LENS and University of Florence1999- : Research fellow, permanent, INFM
11 publications in international journals, 7 publications in books and proceedings, 12 comunications to conferences.Main research interests: Precision spectroscopy, Ultracold atoms and degenerate matter, Matter wave interferometry,Measurement of fundamental constants.
Juergen Stuhler1998-2001: PhD student, University of Konstanz2001- : Post-doc position at LENS and University of Florence
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• COSTS DESCRIPTION
à Total INFN Funding Requested: 320 kEuro
This project includes different parts following different time plans. The requested fundingincludes an initial phase of two years during which most of the expected costs are mainly justifiedby the acquisition of equipment and components and the construction of the gravimeter setup. In thelast period, instead, a large part of the costs are directly related to the optimization of the setup andto the acquisition of the tungsten mass, its characterization, and to the mechanics to hold andprecisely moving it. The last year is essentially dedicated to the actual experiment and to dataanalysis.
In order to achieve the tasks indicated in the project, it is necessary to provide grants andcontracts to scientists willing to participate to the project for an extended time. Finally, travelexpenses have been considered to allow the scientists of the proposing group to visit otherlaboratories, in particular at Yale and Konstanz University, and to participate to conferences andmeetings to present the results.
• OTHER SOURCES OF FUNDING
This research is a new one and no other specific source of funding is available at present. Theresearch groups involved in this project receive funding from their institutions and from INFM,ASI, CNR, European Union.
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