Quantum superpositions and correlations in coupled atomic-molecular BECs

Transcription

1 Quantum superpositions and correlations in coupled atomic-molecular BECs Karén Kheruntsyan and Peter Drummond Department of Physics, University of Queensland, Brisbane, AUSTRALIA Quantum superpositions and correlations in coupled AM BECs.

2 Outline Coupled atom-molecular BECs mechanisms Recent experiments at JILA coherent oscillations in a BEC quantum superposition of atoms and molecules Theory behind the superposition predictions of 1998 revisited... Quantum correlated twin atom-laser beams Quantum superpositions and correlations in coupled AM BECs. 1

3 Why coupled AM BECs Can a molecular BEC form coherently from an atomic BEC? New regimes of non-linear atom optics BOSE-ENHANCED chemistry or superchemistry at ultralow T New microscopic BEC physics to emerge ω ω 1 2 Atomic BEC Molecular BEC Quantum superpositions and correlations in coupled AM BECs. 2

4 Route 1: Raman Photoassociation Pairs of atoms collide, absorb a photon and emit one, giving a ground molecular state Phase locking the two lasers ensures that the conversion is coherent (A BEC M BEC) Drawback: spontaneous emission losses; week freebound couplings γ 2 1 E 3 ω, Ω 2 2 ω Ω, 1 1 2E 1 Molecular BEC δ E 2 Atomic BEC [Wynar et al., Science 287,116 (2)] Quantum superpositions and correlations in coupled AM BECs. 3

5 Route 2: Feshbach Resonance Tunable with an external magnetic field Bound molecular levels become resonant with the energy of free atoms Drawback: large losses due to inelastic collisions Advantages: stronger couplings; tunable atom-atom interactions ε Closed Channel E Open Channel R Quantum superpositions and correlations in coupled AM BECs. 4

6 JILA experiment Rb 85 BEC with a > near ) Feshbach resonance: a a(b) = a bg (1 B B B a scattering length ( a ) 5-5 attractive a< N max = B (G) repulsive a> For na 3 1 (rather than 1), the customary mean-field theory description breaks down New microscopic BEC physics to be expected! Quantum superpositions and correlations in coupled AM BECs. 5

7 Experimental procedure Prepare an atomic BEC at B 166 G, a > Apply a sequence of two fast magnetic-field pulses Measure the number of atoms remaining as a function of t evolve, for different B evolve B (G) B evolve t evolve Pulse #1 Pulse # t (µs) Quantum superpositions and correlations in coupled AM BECs. 6

8 Results [Nature, 417, 529 (May 22)] Remnant Number a t evolve (µs) Frequency (khz) B evolve (G) B evolve (G) Quantum superpositions and correlations in coupled AM BECs. 7

9 Atomic Ramsey interferometry Consider two-level atom ( g, e ); Apply two successive π/2 pulses, R 1 and R 2, at ω ω ge. The first R 1 pulse transforms: g ( g + e ) / 2 e ( g + e ) / 2 After a time delay t evolve, R 2 transforms: g ( g + e e iθ) / 2 e ( g e iθ + e ) / 2 θ = (ω ω ge )t evolve - accumulated phase difference Probability of g g or g e : P g g = (1 + cos θ)/2 P g e = 1 P g g = (1 cos θ)/2 Quantum superpositions and correlations in coupled AM BECs. 8

10 Effective quantum field theory H = [ ] 2 dx i=1,2 2m ˆΨ i 2 + V i (x) ˆΨ ˆΨ i i i H int = χ [ dx ˆΨ2 ˆΨ 1 2 ˆΨ ] 1 + H.c. H self = U ij dx ij 2 ˆΨ ˆΨ ˆΨ i j j ˆΨi ˆΨ 1/2 (t, x) atomic/molecular field operators U 11 a atom-atom S-wave scattering comes from Ũ11(x y) U 11 δ(x y), together with a UV momentum cutoff k max χ atom-molecule coupling (A + A A 2 ) V i trap potentials, including internal energies E i Quantum superpositions and correlations in coupled AM BECs. 9

11 ... apparatus 1... Quantum superpositions and correlations in coupled AM BECs. 1

12 ... apparatus 2... Quantum superpositions and correlations in coupled AM BECs. 11

13 High density regime: 3D matter wave solitons At high densities (mean-field theory applies) wavelike interactions between the entire atomic and molecular BECs are favored Stable 3D matter-wave solitons can form in free space! atomic density molecular density x 1 21 x 1 23 ψ 1 2 (m 3 ) ψ 2 2 (m 3 ) r (µm) 4 5 t (ms) 1 2 r (µm) 4 5 t (ms) 1 [PRL 81, 355 (1998)] Quantum superpositions and correlations in coupled AM BECs. 12

14 Superchemistry oscillations Start with a pure atomic BEC; switch on the coupling Giant coherent oscillations are observed between the atomic and molecular BECs Enhanced chemical reaction rates due to bosonic stimulation at T! [PRL 84, 529 (2)] Quantum superpositions and correlations in coupled AM BECs. 13

15 Low-density regime: Coherent quantum superposition EXACT quantum ground state (for N = 2): [ Ψ (2) ] kmax = ˆb () + dkg(k)â (k)â ( k) k = the eigenstate is a coherent superposition of a molecule with a pair of atoms: dressed molecule Energy eigenvalue E = E m χ2 2 = 2 mr 2. [ U π 2 ] 1 R/m Rk max tan 1 (Rk max ) R - correlation radius; E b = E - binding energy. Quantum superpositions and correlations in coupled AM BECs. 14

16 Approximate quantum many-body solutions Quantum many-body (N > 2) ground state is well approximated by: Ψ (N) = [ ˆb () + kmax k = dkg(k)â (k)â ( k)] N/2 Corresponds to a gas of N/2 independent dressed molecules, with total energy E (N) = N 2 E. The two-particle solution Ψ (2) and the corresponding energy E are keys to understanding the JILA experiment! Quantum superpositions and correlations in coupled AM BECs. 15

17 Binding energy E b vs B? E b (B)/ should give the frequency of oscillations observed (analogous to Ramsey fringes), as interference between atoms and dressed molecules. E b = E m + χ2 2 = 2 mr 2. [ U π 2 ] 1 R/m Rk max tan 1 (Rk max ) can be used for large R, with R 1 k max a bg 1 In JILA experiment, however, R a bg. Must carry out renormalization, to make the theory cut-off independent. Quantum superpositions and correlations in coupled AM BECs. 16

18 Renormalization Prevents UV divergencies as k max Relates bare coupling constants in H to the observed values χ = Γχ, U 11 = ΓU, E m = E + αγ 2 χ 2 where Γ = (1 α U ) 1, α = mk max /(2π 2 2 ), U = 4π a bg /m E = µ(b B ) [Kokkelmans & Holland, cond-mat/2454] Quantum superpositions and correlations in coupled AM BECs. 17

19 E b vs B final result! B = B + 1 µ Eb ( E b + C ) C 2 Eb THEORY E b /h (khz) B (G) EXP. Frequency (khz) B evolve (G) B evolve (G) Quantum superpositions and correlations in coupled AM BECs. 18

20 ... more on quantum correlations... Twin atom-laser beams via dissociation of a molecular BEC produce quantum correlated atomic beams with entangled atom pairs matter-wave analog of parametric down-conversion in nonlinear optics ω (2) χ ω/2 ω/2 strong particle number-difference squeezing is expected applications in precision (sub-shot noise) measurements; new regimes of EPR & Bell correlations with massive particles Quantum superpositions and correlations in coupled AM BECs. 19

21 Photo-dissociation of a molecular BEC start with a BEC of molecular dimers coherently dissociate the molecules into atom pairs, using coherent Raman transitions ω 1 Molecular BEC ω 2 E 2 2 Atom pairs 2E 1 Energy conservation: = 2 k 2 /2m 1 Momentum conservation: ±k = 2m 1 / Quantum superpositions and correlations in coupled AM BECs. 2

22 Twin atomic beams (1D) atomic density molecular BEC ω ω 1 2 t Quantum superpositions and correlations in coupled AM BECs. 21

23 Relative particle number squeezing Variance of fluctuations in particle number difference in two beams: V = [ ( ˆN ˆN / + )] 2 ( ˆN + ˆN + ), = 1 + [ : ( ˆN + ) 2 : ˆN / ˆN+ ] ˆN V 2 1 N τ τ V.7 < 1 (93% squeezing) in this example (losses allowed at 1%; dissociation time 2 ms, ξ 3 µm) Quantum superpositions and correlations in coupled AM BECs. 22

24 SUMMARY Coherent oscillations in BEC number in JILA Feshbach resonance experiment indicate presence of quantum superposition between atoms and molecules Our model quantum field theory gives explicit analytic expression for the superposition state The corresponding binding energy and the experimentally observed frequency of oscillations are in remarkable agreement! Dissociation of a molecular condensate can produce strongly correlated twin atomic beams, with almost perfect squeezing in relative particle number Quantum superpositions and correlations in coupled AM BECs. 23