Forca-G: A trapped atom interferometer for the measurement of short range forces
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1 Forca-G: A trapped atom interferometer for the measurement of short range forces Bruno Pelle, Quentin Beaufils, Gunnar Tackmann, Xiaolong Wang, Adèle Hilico and Franck Pereira dos Santos Sophie Pelisson, Ricardo Messina, Marie-Christine Angonin and Peter Wolf LNE-SYRTE Observatoire de Paris, UMR 8630, CNRS, Université Pierre et Marie Curie Rencontres de Moriond and GPhyS colloqium /03/2011
2 OUTLINE I. Objectives II. III. IV. Principle of the experiment 1. System in a 1D optical lattice 2. Stimulated Raman transitions 3. Induced tunneling Experimental set-up and results 1. Trap loading 2. Bloch frequency measurement 3. Uncertainty on the measure Conclusion and outlook
3 OUTLINE I. Objectives II. III. IV. Principle of the experiment 1. System in a 1D optical lattice 2. Stimulated Raman transitions 3. Induced tunneling Experimental set-up and results 1. Trap loading 2. Bloch frequency measurement 3. Uncertainty on the measure Conclusion and outlook
4 I. Objectives Measurement: Interferometer sensitive to acceleration Acceleration induced by any kind of force Atomic phase difference: ΔΦ ΔU mirror λ lattice /2 with potential: ΔU = Case 1: far from the mirror + vertical geometry g measurement g Case 2: close to the mirror Casimir-Polder force measurement: At range 0,2-10 µm Case 3: C-P force cancelled at 1% Possible deviation of Newton s law: At range 0,2 et 10 µm
5 I. Objectives Measurement: Interferometer sensitive to acceleration Acceleration induced by any kind of force Atomic phase difference: ΔΦ ΔU mirror λ lattice /2 with potential: ΔU = U grav Case 1: far from the mirror + vertical lattice g measurement g Case 2: close to the mirror Casimir-Polder force measurement: At range 0,2-10 µm Case 3: C-P force cancelled at 1% Possible deviation of Newton s law: At range 0,2 et 10 µm U gravity g
6 I. Objectives Measurement: Interferometer sensitive to acceleration Acceleration induced by any kind of force Atomic phase difference: ΔΦ ΔU with potential: ΔU = U grav + U CP Case 1: far from the mirror + vertical lattice g measurement Case 2: close to the mirror Casimir-Polder force measurement: At range 0,2-10 µm Case 3: C-P force cancelled at 1% Possible deviation of Newton s law: At range 0,2 et 10 µm Predicted in 1948: H.G.B. Casimir and D.Polder, Phys. Rev. 73, 360 (1948) - current uncertainty of > 10 % - aimed uncertainty better than 1 % r U CP atom 3 c r 0 : electrical atomic polarisability
7 I. Objectives Measurement: Interferometer sensitive to acceleration Acceleration induced by any kind of force Atomic phase difference: ΔΦ ΔU with potential: ΔU = U grav + U CP + U Yuk Case 1: far from the mirror + vertical lattice g measurement Case 2: close to the mirror Casimir-Polder force measurement: At range 0,2-10 µm Case 3: C-P force cancelled at 1% Possible deviation of Newton s law: (between the atom and the surface) At range 0,2 et 10 µm Unification theories: - forecast hypothetic new interactions - which can be generalized under the so-called parametric Yukawa potential GM 1M 2 U Yuk 1 e r : deviation amplitude λ: deviation range r
8 I. Objectives Measurement: Interferometer sensitive to acceleration Acceleration induced by any kind of force Atomic phase difference: ΔΦ ΔU Constraints on Yukawa potential on the (,λ) plane at short range: with potential: ΔU = U grav + U CP + U Yuk Case 1: far from the mirror + vertical lattice g measurement Case 2: close to the mirror Casimir-Polder force measurement: At range 0,2-10 µm Case 3: C-P force cancelled at 1% Possible deviation of Newton s law: (between the atom and the surface) At range 0,2 et 10 µm R. Messina, S. Pelisson, M.C. Angonin and P. Wolf, arxiv: v1 (2011)
9 OUTLINE I. Objectives II. III. IV. Principle of the experiment 1. System in a 1D optical lattice 2. Stimulated Raman transitions 3. Induced tunneling Experimental set-up and results 1. Trap loading 2. Bloch frequency measurement 3. Uncertainty on the measure Conclusion and outlook
10 g II. Principle of the experiment 1. System in a 1D optical lattice Requirements: 1. To get localized atoms 2. To know precisely distance between the surface and the atoms 3. To allow precise spatial control Corresponding system: Periodic potential (standing wave): for 3. With linear potential (g): for 1. and 2. Hamiltonian: mirror Eigenstates: Wannier-Stark states, W m Separated by Δ g Lifetime of metastable state: s at U=3Er
11 II. Principle of the experiment 1. System in a 1D optical lattice Requirements: 1. To get localized atoms 2. To know precisely distance between the surface and the atoms 3. To allow precise spatial control g Corresponding system: Periodic potential (standing wave) With linear potential (g): for 1. and 2. Hamiltonian: E Trapped atoms: are delocalised Eigenstates: Wannier-Stark states, W m Separated by Δ g Lifetime of metastable state: s at U=3Er z
12 II. Principle of the experiment 1. System in a 1D optical lattice Requirements: 1. To get localized atoms 2. To know precisely distance between the surface and the atoms 3. To allow precise spatial control g Corresponding system: Periodic potential (standing wave) With linear potential (g) Hamiltonian: E Trapped atoms: Linear potential gradient remove the degeneracy Eigenstates: Allow localized atoms and precise position (1.&2.) Wannier-Stark states, W m Separated by Δ g Lifetime of metastable state: s at U=3Er z
13 II. Principle of the experiment 1. System in a 1D optical lattice Requirements: 1. To get localized atoms 2. To know precisely distance between the surface and the atoms 3. To allow precise spatial control Corresponding system: Periodic potential (standing wave) With linear potential (g) Trapping a 2-level atom 5 2 S 1/2 F=2 m F =0 e n HFS = GHz Hamiltonian: 5 2 S 1/2 F=1 m F =0 g 87 Rb Eigenstates: Wannier-Stark states, W m separated by Δ g Lifetime of metastable state: s at U=3Er
14 II. Principle of the experiment 1. System in a 1D optical lattice Requirements: 1. To get localized atoms 2. To know precisely distance between the surface and the atoms 3. To allow precise spatial control Corresponding system: Periodic potential (standing wave) With linear potential (g) Trapping a 2-level atom Hamiltonian: H ext 2 kˆ 2m 2 a U cos 2k zˆ m gzˆ lattice P. Wolf et al., PRA 75, (2007) Eigenstates: Wannier-Stark states, W m separated by the Bloch frequency Δ g Lifetime of metastable state: s at lattice depth U=3Er a
15 II. Principle of the experiment 1. System in a 1D optical lattice Requirements: 1. To get localized atoms 2. To know precisely distance between the surface and the atoms 3. To allow precise spatial control Corresponding system: Periodic potential (standing wave) With linear potential (g) Trapping a 2-level atom e W m-1 W m W m+1 n HFS = GHz W m+2 Hamiltonian: H ext 2 kˆ 2m 2 a U cos 2k zˆ m gzˆ lattice P. Wolf et al., PRA 75, (2007) Eigenstates: Wannier-Stark ladder, W m separated by the Bloch frequency n B Lifetime of metastable state: s at lattice depth U = 3E r a g n B = m a g λ lattice /2h = 569 Hz
16 II. Principle of the experiment 2. Stimulated Raman transitions Coupling realized with stimulated Raman transitions Coupling in the same well: Microwave Co-propagating Raman impulsion Or contra-propagating Raman impulsion Copropagating : k eff = k 1 k 2 k 1 k 2 Coupling between wells: Contra-propagating Raman impulsion (k eff 2k Ram ) Efficient when k eff k lattice Resonance: And when Raman frequency detuned by D g Contrapropagating : k eff = k 1 + k 2 k 1 k 2
17 II. Principle of the experiment 3. Induced tunneling Coupling realized with stimulated Raman transitions Coupling in the same well: Microwave Co-propagating Raman impulsion Or contra-propagating Raman impulsion e n HFS W m-1 W m W m+1 0 W m+2 Coupling between wells: Contra-propagating Raman impulsion (k eff 2k Ram ) Efficient when k eff k lattice Resonance: when Raman frequency is detuned by D g g n B
18 II. Principle of the experiment 3. Induced tunneling Coupling realized with stimulated Raman transitions Coupling in the same well: Microwave Co-propagating Raman impulsion Or contra-propagating Raman impulsion 2 e W m-1 W m W m+1 n HFS W m+2 2 Coupling between wells: Contra-propagating Raman impulsion (k eff 2k Ram ) Efficient when k eff k lattice g n B Resonance: when Raman frequency is detuned by n B Dn Raman = n HFS + Dn n B Stimulated Raman transitions: allow precise spatial control (requirement 3.)
19 II. Principle of the experiment 3. Induced tunneling Coupling realized with stimulated Raman transitions Coupling in the same well: Microwave Co-propagating Raman impulsion Or contra-propagating Raman impulsion 2 e W m-1 0 n HFS 1 W m W m+1 W m Coupling between wells: Contra-propagating Raman impulsion (k eff 2k Ram ) Efficient when k eff k lattice Resonance: when Raman frequency is detuned by n B Dn Raman = n HFS + Dn n B g Coupling: by translation operator in momentum space Dn n B ik z Wm e eff ˆ Wm Dn with m: well index Dn: coupling well difference (integer)
20 OUTLINE I. Objectives II. III. IV. Principle of the experiment 1. System in a 1D optical lattice 2. Stimulated Raman transitions 3. Induced tunneling Experimental set-up and results 1. Trap loading 2. Bloch frequency measurement 3. Uncertainty on the measure Conclusion and outlook
21 III. Experimental set-up and results 1. Trap loading a. Cold atoms generation To cool atoms to trap them 3D MOT: 10 7 atoms at 2µK Waveplate b. Confinements Longitudinal: Blue detuned standing wave Verdi: λ lattice = 532 nm P max = 12 W w = 600 µm on atoms Trapping into the nodes (I=0) Transverse: Red detuned IR: λ = 1064 nm P max = 20 W w = 200 µm on atoms Trapping into the beam center Atoms 87 Rb Raman lasers Dichroic Mirror Mirror CCD Camera
22 III. Experimental set-up and results 1. Trap loading a. Cold atoms generation To cool atoms to trap them 3D MOT: 10 7 atoms at 2µK IR transverse trap Waveplate b. Confinements Longitudinal: Blue detuned standing wave Verdi: λ lattice = 532 nm P max = 12 W w = 600 µm on atoms Trapping into the nodes (I=0) Transverse: Red detuned IR: λ = 1064 nm P max = 20 W w = 200 µm on atoms Trapping into the beam center Raman lasers Atoms Dichroic Mirror Verdi longitudinal trap Mirror CCD Camera
23 III. Experimental set-up and results 1. Trap loading a. Cold atoms generation To cool atoms to trap them 3D MOT: 10 7 atoms at 2µK b. Confinements Longitudinal: Blue detuned standing wave Verdi: λ lattice = 532 nm P max = 12 W w = 600 µm on atoms Trapping into the nodes (I=0) IR transversal trap Waveplate Dichroic Mirror Atoms Mirror Transverse: Red detuned IR: λ = 1064 nm P max = 20 W w = 200 µm on atoms Trapping into the beam center Verdi longitudinal trap
24 III. Experimental set-up and results 1. Trap loading a. Cold atoms generation To cool atoms to trap them 3D MOT: 10 7 atoms at 2µK b. Confinements Longitudinal: Blue detuned standing wave Verdi: λ lattice = 532 nm P max = 12 W w = 600 µm on atoms Trapping into the nodes (I=0) IR transversal trap Waveplate Dichroic Mirror Atoms Mirror Transverse: Red detuned IR: λ = 1064 nm P max = 20 W w = 200 µm on atoms Trapping into the beam center Trapping life time: 1s For longer interrogation time Verdi longitudinal trap
25 III. Experimental set-up and results 1. Trap loading c. Preparation IR transversal trap Preparation in one state: 5 2 S 1/2 F=1 m F =0 g Waveplate d. Atom interrogation Raman: λ Ram = 780nm, P max = 50mW, w = 1cm on atoms contra-propagating Transition in the other state: Dichroic Mirror Mirror e. Detection CCD camera: image the atoms after a fluorescence pulse Time of Flight measurement: Detection by state selection fluorescence Giving state populations N g, N e Then the transition probability is: Atoms Verdi longitudinal trap
26 III. Experimental set-up and results 1. Trap loading c. Preparation IR transversal trap Preparation in one state: 5 2 S 1/2 F=1 m F =0 g Waveplate d. Atom interrogation Raman: λ Ram = 780nm, P max = 50mW, w = 1cm on atoms Contra-propagating Transition in the other state: 5 2 S 1/2 F=2 m F =0 e Dichroic Mirror Mirror e. Detection CCD camera: image the atoms after a fluorescence pulse Time of Flight measurement: Detection by state selection fluorescence Giving state populations N g, N e Then the transition probability is: Atoms Raman lasers Verdi longitudinal trap
27 III. Experimental set-up and results 1. Trap loading c. Preparation IR transversal trap Preparation in one state: 5 2 S 1/2 F=1 m F =0 g Waveplate d. Atom interrogation Raman: λ Ram = 780nm, P max = 50mW, w = 1cm on atoms Contra-propagating Transition in the other state: 5 2 S 1/2 F=2 m F =0 e Dichroic Mirror Mirror e. Detection CCD camera: Image the atoms after a fluorescence pulse Time of Flight measurement: Detection by state selection fluorescence Giving state populations N g, N e Then the transition probability is: Fluorescence pulse CCD Camera Verdi longitudinal trap
28 III. Experimental set-up and results 1. Trap loading c. Preparation Preparation in one state: 5 2 S 1/2 F=1 m F =0 g Waveplate d. Atom interrogation Raman: λ Ram = 780nm, P max = 50mW, w = 1cm on atoms Contra-propagating Transition in the other state: 5 2 S 1/2 F=2 m F =0 e Dichroic Mirror Mirror e. Detection CCD camera: Image the atoms after a fluorescence pulse Time of Flight measurement: Detection by state selection fluorescence Giving state populations N g, N e Then the transition probability is: Atoms
29 III. Experimental set-up and results 1. Trap loading c. Preparation Preparation in one state: 5 2 S 1/2 F=1 m F =0 g Waveplate d. Atom interrogation Raman: λ Ram = 780nm, P max = 50mW, w = 1cm on atoms Contra-propagating Transition in the other state: 5 2 S 1/2 F=2 m F =0 e Dichroic Mirror Mirror e. Detection CCD camera: Image the atoms after a fluorescence pulse Time of Flight measurement: Detection by state selection fluorescence Giving state populations N g, N e Then the transition probability is: Atoms
30 III. Experimental set-up and results 1. Trap loading c. Preparation Preparation in one state: 5 2 S 1/2 F=1 m F =0 g Waveplate d. Atom interrogation Raman: λ Ram = 780nm, P max = 50mW, w = 1cm on atoms Contra-propagating Transition in the other state: 5 2 S 1/2 F=2 m F =0 e Dichroic Mirror Mirror e. Detection CCD camera: Image the atoms after a fluorescence pulse Time of Flight measurement: Detection by state selection fluorescence Giving state populations N g, N e Then the transition probability is: P e N g Fluorescence pulse Ne N e
31 III. Experimental set-up and results 2. Bloch frequency measurement Raman spectroscopy: single Raman pulse of duration t = 8 ms tuning Dn Raman = n HFS + Dn n B measuring the transition probability P e P e Dn = n B = 569 Hz P e N g Ne N e Dn Raman - n HFS
32 III. Experimental set-up and results 2. Bloch frequency measurement Ramsey-Raman interferometer: two Raman pulses of duration t /2 = 5 ms, seperated by T Ramsey = 100 ms tuning Dn Raman = n HFS + Dn n B measuring the transition probability P e Raman power T Ramsey /2 /2 t
33 III. Experimental set-up and results 2. Bloch frequency measurement Ramsey-Raman interferometer: two Raman pulses of duration t /2 = 5 ms, seperated by T Ramsey = 100 ms tuning Dn Raman = n HFS + Dn n B measuring the transition probability P e Raman power T Ramsey 1/T Ramsey /2 /2 t To improve precision on the central fringe
34 III. Experimental set-up and results 3. Uncertainty on the measure Ramsey-Raman interferometer: T Ramsey = 400 ms, t /2 = 5 ms Integration on peaks: Dn = +6 and Dn = -6 Drifts: for both peaks drift suppression via half difference High integration stability over 10,000 s Relative sensitivity on Bloch frequency: (n B )/n B = g/g = at 1 s => For Casimir-Polder measurement: 1 % uncertainty for L = s t -1/2
35 III. Experimental set-up and results 3. Uncertainty on the measure Ramsey-Raman interferometer: T Ramsey = 400 ms, t /2 = 5 ms Integration on peaks: Dn = +6 and Dn = -6 Drifts: for both peaks drift suppression via half difference High integration stability over 10,000 s Relative sensitivity on Bloch frequency: (n B )/n B = g/g = at 1 s t -1/2 => For Casimir-Polder measurement: 1 % uncertainty for L = 5 µm at 1000s
36 OUTLINE I. Objectives II. III. IV. Principle of the experiment 1. System in a 1D optical lattice 2. Stimulated Raman transitions 3. Induced tunneling Experimental set-up and results 1. Trap loading 2. Bloch frequency measurement 3. Uncertainty on the measure Conclusion and outlook
37 IV. Conclusion and outlook So far: First demonstration of a trapped atom interferometer setup Using Raman transitions for coupling lattice states (Wannier-Stark states) Until now, far from the mirror surface Characterization of the main noise sources (in progress) To be done: Mounting the mirror inside the vacuum chamber To realize a single site addressing function Increase of atom density To implement an atom cloud elevator : to avoid mirror surface pollution and for differential measurements in different distances
38 Thank you for your attention Thanks for financial supports :
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