Bloch oscillations of ultracold-atoms and Determination of the fine structure constant
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1 Bloch oscillations of ultracold-atoms and Determination of the fine structure constant Pierre Cladé P. Cladé Bloch oscillations and atom interferometry Sept., / 28
2 Outlook Bloch oscillations of ultracold atoms : a tool for transferring photon momentum to atoms Experiment using Bloch oscillations : Measurement of the atom recoil velocity, determination of the fine structure constant α, test of QED Measurement of the acceleration of gravity Large momentum transfer beamsplitter See also : International School of Physics Enrico Fermi, Bloch oscillations in atom interferometry, P. Cladé. arxiv: P. Cladé Bloch oscillations and atom interferometry Sept., / 28
3 Atom light interaction 1 P. Cladé Bloch oscillations and atom interferometry Sept., / 28
4 Atom light interaction 1 2 Spontaneous emission P. Cladé Bloch oscillations and atom interferometry Sept., / 28
5 Atom light interaction 1 P. Cladé Bloch oscillations and atom interferometry Sept., / 28
6 Atom light interaction 1 2 Two photon transition to supress spontaneous emission. Same internal state Two different internal states P. Cladé Bloch oscillations and atom interferometry Sept., / 28
7 Succession of stimulated Raman transitions (same hyperfine level) Coherent acceleration of atoms Bloch oscillations δ = ν 1 ν 2 t Adiabatic passage : acceleration of the atoms Energy The atoms are placed in an accelerated standing wave : in its frame, they are submitted to an inertial force Bloch oscillations in a periodic potential Ben Dahan, et al., PRL 76, (1996) (group of C. Salomon, LKB, Paris) P. Cladé Bloch oscillations and atom interferometry Sept., / 28
8 Bloch oscillations in an optical lattice How to cross the transition? Change the detuning (ω 1 ω 2 ) Change the quasi-momentum with a force : q(t) = q(0) + Fd t P. Cladé Bloch oscillations and atom interferometry Sept., / 28
9 Bloch oscillations in an optical lattice How to cross the transition? Change the detuning (ω 1 ω 2 ) Change the quasi-momentum with a force : q(t) q(t) = q(0) = q(0) + Fd + Fd t t is always true Rotation of the quasimomentum If the adiabatic criteria is fulfilled : Bloch oscillations Oscillation of the velocity Oscillation of the position Period : T Bloch = 2 k F P. Cladé Bloch oscillations and atom interferometry Sept., / 28
10 Atom in an accelerated lattice v = (ν 1 ν 2 )/2k Light shifts : periodic potential U(x, t) = U 0 2 cos(2k(x vt)) Position Velocity Position Velocity P. Cladé Bloch oscillations and atom interferometry Sept., / 28
11 Atom in an accelerated lattice v = (ν 1 ν 2 )/2k Light shifts : periodic potential U(x, t) = U 0 2 cos(2k(x vt)) Position Wannier function (center at v=0) Velocity Position Velocity P. Cladé Bloch oscillations and atom interferometry Sept., / 28
12 Atom in an accelerated lattice v = (ν 1 ν 2 )/2k Light shifts : periodic potential U(x, t) = U 0 2 cos(2k(x vt)) Position Wannier function (center at v=0) Velocity Position Velocity P. Cladé Bloch oscillations and atom interferometry Sept., / 28
13 Atom in an accelerated lattice v = (ν 1 ν 2 )/2k Light shifts : periodic potential U(x, t) = U 0 2 cos(2k(x vt)) Position Velocity Position Wannier function Acceleration Velocity P. Cladé Bloch oscillations and atom interferometry Sept., / 28
14 Atom in an accelerated lattice v = (ν 1 ν 2 )/2k Light shifts : periodic potential U(x, t) = U 0 2 cos(2k(x vt)) Position Wannier function Velocity Position Wannier function (center at v~2nvr) Acceleration Velocity P. Cladé Bloch oscillations and atom interferometry Sept., / 28
15 Atom in an accelerated lattice v = (ν 1 ν 2 )/2k Light shifts : periodic potential U(x, t) = U 0 2 cos(2k(x vt)) Position Wannier function Velocity Position Wannier function (center at v~2nvr) Acceleration Velocity P. Cladé Bloch oscillations and atom interferometry Sept., / 28
16 Atom in an accelerated lattice v = (ν 1 ν 2 )/2k Light shifts : periodic potential U(x, t) = U 0 2 cos(2k(x vt)) Position Wannier function Velocity Position Wannier function (center at v~2nvr) Acceleration Velocity P. Cladé Bloch oscillations and atom interferometry Sept., / 28
17 Bloch oscillations in the frame of the lattice H = ˆp2 2 F ˆx + U 0 cos(2kx) (1) 2 Quasi-momentum = phase-shift between two sites φ(t) = E t T Bloch = 2 k F In a deep lattice, atoms are not moving, but the phase evolves. By adiabatically switching off the lattice, all site will interfere and recombine to a single momentum between k and k. P. Cladé Bloch oscillations and atom interferometry Sept., / 28
18 Bloch oscillations Bloch oscillations are very efficient: It is not sensitive to the initial velocity of atoms (provided that it fits within the first Brillouin zone) It is not sensitive to variation of the intensity (provided that the intensity is above a given threshold) It works also in the tight binding limit with a very good efficiency Some applications : Measurement of the recoil velocity Measurement of g Large Momentum Transfer Beamsplitter P. Cladé Bloch oscillations and atom interferometry Sept., / 28
19 Introduction to atom interferometry Doppler effect ( δ = k1 k ) 2 v Selection of a subrecoil velocity distribution t P. Cladé Bloch oscillations and atom interferometry Sept., / 28
20 Introduction to atom interferometry Doppler effect ( δ = k1 k ) 2 v Selection of a subrecoil velocity distribution Measurement of the final velocity distribution Blow away beam??? t P. Cladé Bloch oscillations and atom interferometry Sept., / 28
21 Introduction to atom interferometry Doppler effect ( δ = k1 k ) 2 v Selection of a subrecoil velocity distribution Measurement of the final velocity distribution Blow away beam??? t P. Cladé Bloch oscillations and atom interferometry Sept., / 28
22 Atom interferometry Rabi t. P. Cladé Bloch oscillations and atom interferometry Sept., / 28
23 Atom interferometry Rabi t. Method of Separated Oscillatory Field (Ramsey) Replace a π pulse by two π/2 pulses. t P. Cladé Bloch oscillations and atom interferometry Sept., / 28
24 Atom interferometry Rabi t. Method of Separated Oscillatory Field (Ramsey) Replace a π pulse by two π/2 pulses. t Horizontal and vertical blow away beam Raman Raman 10 ms 10 ms x Ch.J. Bordé ( ) t P. Cladé Bloch oscillations and atom interferometry Sept., / 28 t
25 Measring the recoil velocity Horizontal and vertical blow away beam Raman Raman 10 ms 10 ms t P. Cladé Bloch oscillations and atom interferometry Sept., / 28
26 Measring the recoil velocity Horizontal and vertical blow away beam Raman Raman 10 ms 10 ms t 100 Hz δsel - δ mes P. Cladé Bloch oscillations and atom interferometry Sept., / 28
27 Measring the recoil velocity Horizontal and vertical blow away beam Raman Bloch Raman 10 ms 10 ms Acceleration t P. Cladé Bloch oscillations and atom interferometry Sept., / 28
28 Measring the recoil velocity Horizontal and vertical blow away beam Raman Bloch Raman 10 ms 10 ms Acceleration t P. Cladé Bloch oscillations and atom interferometry Sept., / 28
29 Measring the recoil velocity Horizontal and vertical blow away beam Raman Bloch Raman 10 ms 10 ms Acceleration t P. Cladé Bloch oscillations and atom interferometry Sept., / 28
30 Measring the recoil velocity Horizontal and vertical blow away beam Bloch Raman Bloch Raman 10 ms 10 ms Acceleration Deceleration t P. Cladé Bloch oscillations and atom interferometry Sept., / 28
31 Measring the recoil velocity Horizontal and vertical blow away beam Bloch Raman Bloch Raman 10 ms 10 ms Elevator Acceleration Deceleration t z [m] T [ms] P. Cladé Bloch oscillations and atom interferometry Sept., / 28
32 Measring the recoil velocity Horizontal and vertical blow away beam Bloch Raman Bloch Raman 10 ms 10 ms Elevator Acceleration Deceleration t 100 Hz δsel - δ mes δsel - δ mes P. Cladé Bloch oscillations and atom interferometry Sept., / 28
33 Results (2010) 170 measurements (14 hours) Each measurement : (h/m) and (α) Relative uncertainty on h/m : and on α. P. Cladé Bloch oscillations and atom interferometry Sept., / 28
34 Error Budget Uncertainty Source Correction Laser frequencies 1.3 Beams alignment Wavefront curvature and Gouy phase nd order Zeeman effect Gravity gradient Light shift (one photon transition) 0.1 Light shift (two photon transition) 0.01 Light shift (Bloch oscillations) 0.5 Index of refraction atomic cloud and atom interactions 2.0 Global systematic effects Statistical uncertainty 2.0 Rydberg constant and mass ratio 2.2 Total uncertainty 6.6 P. Cladé Bloch oscillations and atom interferometry Sept., / 28
35 Error Budget Uncertainty Source Correction Laser frequencies 1.3 Beams alignment Wavefront curvature and Gouy phase Wavefront 2nd order curvature Zeeman effect and Gouy phase shift Gravity gradient Light shift (one What photon is the transition) momentum of a photon? 0.1 p Light = φ zshift where (two φ photon is the phase transition) of the laser beam p Light = k shift holds (Bloch only for oscillations) perfect plane-wave. 0.5 For Index a Gaussian of refraction beam atomic : cloud and atom interactions φ 2.0 Global systematic effects z = 1 ( 4 2k w 2 4r 2 w 4 + r 2 k 2 ) R (2) Statistical uncertainty 2.0 where Rydberg w isconstant the waist and of mass the beam, ratio R the wavefromnt curvature 2.2 and r the Total distance uncertainty from the propagation axes of the beam. 6.6 P. Cladé Bloch oscillations and atom interferometry Sept., / 28
36 Error Budget Uncertainty Source Correction Wavefront curvature and Gouy phase shift Laser frequencies 1.3 What is the momentum of a photon? Beams alignment A Shack-Hartmann analyzer is used to characterize the wave front. Wavefront curvature and Gouy phase nd order Zeeman effect Gravity gradient Flat Wavefront Light shift (one photon transition) 0.1 Light shift (two photon transition) 0.01 Light shift (Bloch oscillations) 0.5 Index of refraction atomic cloud and atom interactions 2.0 Global systematic effects Statistical uncertainty 2.0 Lenslet array CCD screen Rydberg constant and mass ratio Spot pattern 2.2 Total uncertainty 6.6 P. Cladé Bloch oscillations and atom interferometry Sept., / 28
37 Error Budget Uncertainty Source Correction Wavefront curvature and Gouy phase shift Laser frequencies 1.3 What is the momentum of a photon? Beams alignment A Shack-Hartmann analyzer is used to characterize the wave front. Wavefront curvature and Gouy phase nd order Zeeman effect Gravity gradient Distorted Wavefront Light shift (one photon transition) 0.1 Light shift (two photon transition) 0.01 Light shift (Bloch oscillations) 0.5 Index of refraction atomic cloud and atom interactions 2.0 Global systematic effects Statistical uncertainty 2.0 Lenslet array CCD screen Rydberg constant and mass ratio Spot pattern 2.2 Total uncertainty 6.6 P. Cladé Bloch oscillations and atom interferometry Sept., / 28
38 Error Budget Uncertainty Source Correction Laser frequencies 1.3 Beams alignment Wavefront curvature and Gouy phase Wavefront 2nd order curvature Zeeman effect and Gouy phase shift Gravity gradient w = 3.6 mm Light shift (one photon transition) 0.1 Light R > shift 30(two m photon transition) 0.01 Largest Light shift systematic (Blocheffect oscillations) : Index of refraction atomic cloud and atom interactions 2.0 Global systematic effects Statistical uncertainty 2.0 Rydberg constant and mass ratio 2.2 Total uncertainty 6.6 P. Cladé Bloch oscillations and atom interferometry Sept., / 28
39 Error Budget Uncertainty Source Correction Laser frequencies 1.3 Beams alignment Wavefront curvature and Gouy phase nd order Zeeman effect Gravity gradient Light shift (one photon transition) 0.1 Light shift (two photon transition) 0.01 Light shift (Bloch oscillations) 0.5 Index of refraction atomic cloud and atom interactions 2.0 Global systematic effects Statistical uncertainty 2.0 Rydberg constant and mass ratio 2.2 Total uncertainty 6.6 P. Cladé Bloch oscillations and atom interferometry Sept., / 28
40 Measurements of α First verification of the muonic and hadronic contributions to a e P. Cladé Bloch oscillations and atom interferometry Sept., / 28 hr c = 1 2 m ec 2 α 2 LKB-10 (Paris) : α 1 = (91) [ ] a e = (78) HarvU-08 : a e = (28) 7 ae - UW-87 6 h/m(cs) StanfU-02 5 h/m(rb) LKB-06 4 CODATA h/m(rb) - LKB-08 2 ae - HarvU-08 1 ae - HarvU-08 + Kinoshita 2012 h/m - LKB ( α ) ( α ) 2 ( α ) 3 ( α ) 4 ( α ) 5 ( me ) ( me ) π π π π π m µ m τ a(weak) a(hadron)
41 Mesurement of gravity Cold atom gravimeter : sensitivity scale as T 2 How to build compact gravimeter? F. Impens et al., Applied Physics B 84, 603 (2006) J. H. Hughes et al., Phys. Rev. Lett. 102, (2009) N. Poli et al., Phys. Rev. Lett. 106, (2011) P. Cladé et al., Europhys. Lett. 71, 730 (2005) R. Charrière et al., Phys. Rev. A 85, (2012) B. Pelle et al., Rev. A 87, (2013) Measurement of the Bloch period Measuring the position/velocity with time of flight methods Long interogation time Transverse confinement in the lattice Control of atom-atom interactions Atomic levitation using Bloch oscillations P. Cladé Bloch oscillations and atom interferometry Sept., / 28
42 Bloch oscillations in the frame of the lattice H = ˆp2 2 F ˆx + U 0 cos(2kx) (3) 2 Quasi-momentum = phase-shift between two sites φ(t) = E t T Bloch = 2 k F In a deep lattice, atoms are not moving, but the phase evolves. By adiabatically switching off the lattice, all site will interfere and recombine to a single momentum between k and k. P. Cladé Bloch oscillations and atom interferometry Sept., / 28
43 Mesurement of gravity z Raman Raman Bloch (N oscillations) Raman Raman b,p+hk eff x x a,p+2nhk a,p pushing beam N.T B T T' T t P. Cladé Bloch oscillations and atom interferometry Sept., / 28
44 Mesurement of gravity T R Impulsion Raman π/2 T B N Oscillations de Bloch T 2Nv r = gt B P. Cladé Bloch oscillations and atom interferometry Sept., / 28
45 Compact gravimeter N=50, M=4 and T =230 ms h < 5mm g = 1 ( T 2NM kb δ ) R m Rb k 1 + k 2 k 1 et k 2 : Raman wavevectors and k B : Bloch wavevector g gal [µgal] Tide effect Determination of g g/g=4, sur 4 min Width of the atomic cloud Vibrations [µgal] Time [h] P. Cladé Bloch oscillations and atom interferometry Sept., / 28
46 Using Bloch oscillation for Large Momentum Transfer Beamsplitter The sensitivity (in velocity) of an interferometer is proportional to the distance between the two arms Increase the duration between the pulses Increase the splitting of the beamsplitter Large momentum beamsplitter based on BOs Conventional separation (Raman transition, Bragg diffraction) Acceleration of one arm of the interferometer using Bloch oscillations P. Cladé Bloch oscillations and atom interferometry Sept., / 28
47 Using Bloch oscillation for Large Momentum Transfer Beamsplitter P. Cladé Bloch oscillations and atom interferometry Sept., / 28
48 Using Bloch oscillation for Large Momentum Transfer Beamsplitter P. Cladé et. al. Theoretical analysis of a large momentum beamsplitter using Bloch oscillations EPJ D, 2010, 59, P. Cladé Bloch oscillations and atom interferometry Sept., / 28
49 Large Momentum Beam Splitter P. Cladé Bloch oscillations and atom interferometry Sept., / 28
50 Preliminary study Distance [µm] P. Cladé et al. Large Momentum Beam Splitter Using Bloch Oscillations, Phys. Rev. Lett., 2009, 102, Key point : contrast of the fringes Large Momentum Beamsplitter T[ms] 2 recoils beamspitter There is an inhomogeneous broadening due to the transverse velocity of atoms We need a colder atomic source (below µk) P. Cladé Bloch oscillations and atom interferometry Sept., / 28
51 New project High precision atom interferometry using large momentum transfer beamsplitter Evaporative cooling (technique used for BEC) Dipole trap Shot noise limited detection Vibration isolation Magnetic shield Optical frequency measurement Wavefront design Design of a setup to reach the accuracy Main systematic effects : Atom-atom interaction Wavefront curvature and Gouy phase shift P. Cladé Bloch oscillations and atom interferometry Sept., / 28
52 Ph.D Students R. Battesti (2003) P. Cladé (2005) M. Cadoret (2008) R. Bouchendira(2012) M. Andia R. Jannin C. Courvoisier Postdoc E. de Mirandes ( ) Permanents C. Schwob L. Julien P. Cladé S. Guellati-Khélifa F. Nez F. Biraben P. Cladé Bloch oscillations and atom interferometry Sept., / 28
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