Distinguishable Fermions? Ultracold Fermions

Transcription

1 Distinguishable Fermions? Identical? + Despite decoherence, Bosons and Fermion often appear to be quantum mechanically identical. Ultracold Fermions At ultracold temperatures, only s wave scattering. Antisymmetric wavefunction no scattering of identical superpositions! σ = Decoherence distinguishable fermions collisions σ + No hift! Despite being distinguishable, fermions act as if they re indistinguishable! [H light,v ]= Fermions are Universally Immune to Collisions! Zwierlein, Hadzibabic, Gupta, & Ketterle, PRL 3 3

2 P Bosons & the Factor of Controversy Identical bosons in different states are distinguishable. P σ = 4πaP Exchange symmetry of identical bosons. σ = 4πa P σ = 4πa The Mystery of the P Ramsey Fringe that Didn t Chirp Decoherence destroys interstate coherence. No exchange symmetry m Δ ν = n( app a) + ( ap app a)( np n) hv Δν Exchange symmetry of identical superpositions. Harber, Lewandowski, McGuirk, & Cornell, PRA, ICAP n P n s-wave Frequency hifts & pin Waves in Fermion Clocks s-wave frequency shift of fermions Experiments: 87 Rb Chip & 6 Li Fermion Clock Observation of distinguishing characteristics Tune scattering length near an s-wave Feshbach resonance trong Interactions coherence & collision shifts cattering-induced tunneling. pin waves Penn tate Eric Hazlet Kunyun Ye Ron tites Kurt Gibble Ken O Hara upport from ANR, AQUTE, DARPA, EMRP IND4, IFRAF, NF, ONR, la Ville de Paris, Penn tate, & loan. Christian Deutsch Jakob Reichel θ θ a = 4 a Obs. Paris Wilfried Maineult Peter Rosenbusch

3 Optical Clock Fermion Collisions Fermions are universally immune to collisions. Campbell & Ye observed a collision shift for fermions. Treated shift as n n P. h a () Δ ν? = P g ( n n P) m [H light,v P ] for clock fields with fast spatial variations. Observed r & Yb shifts are p-wave Is h Δν = μ μ? How can a spatially uniform field change the spatial pair correlation function g ()? Δν (Hz/n) μk 3 μk Final n (detuning) Zwierlein, Hadzibabic, Gupta, & Ketterle, PRL 3 Lemke, Oates, PRL 9 Campbell, Julienne, Ye, cience 9 Lemke, Oates, Ludlow, PRL /5/3-5 { ψa ( r ) ψb ( r) } r + r Ω ΔΩ Fermion Clock Collision hift Many particles are sum of pair-wise effects Basis inglet and Triplet states of atoms: g a n P ψ r ψ r { a ( ) b ( ) } + a π θ b θ π Ω=Ω θ e i Δω at a T Ω=Ω e i Δω bt b θ a =4a Δ ν = ( Δθ) ( Δθ) ( θ) ( ) ( ) g sin sin cos π sin θ sin θ θ KG, PRL 9 Hazlett, Zhang, tites, KG, O Hara PRL 3

4 + Ω ΔΩ Δθ = s=; identical fermions Δν is not proportional to n n P (excitation fraction) n np cos( θ ) = n No shift for Δθ = No shift for θ = π KG, PRL 9 Fermion Clock Collision hift g a n P a π θ b Δ ν = π Ω=Ω θ e i Δω at a T Ω=Ω e i Δω bt b θ ( Δθ) ( Δθ) ( θ) ( ) ( ) g sin sin cos π sin θ sin θ θ θ Hazlett, Zhang, tites, KG, O Hara PRL 3 a =4a Optical Clock Fermion Collisions No collision shift for θ = π Connect to free space scattering. γ g + δ e Entangled & P scattered s-wave One particle gets a large positive shift, the other negative α g + β e.6 Δν/g Δ θ = % θ θ = θ Δν a / Ramsey θ + θ π Rabi Rabi is the same as Ramsey. Absence of shift is due to Bloch rotation readout of phase..6 Δν b / Hart, Xu, Legere, & KG, Nature 7 KG, PRL 9 /5/3-8

5 & 87 Rb is a fermion in a clock All 3 scattering lengths are nearly equal. Overall energy shift of triplet states is always. Decoherence appears via singlet states Δν P + t P u PP d Ω ΔΩ s P ( ) g = g + g PP Δ g = g g δ g = g g g P PP P PP ( ) ( )( ) πδ ν = n g g + g g g n n PP P PP P ( Δθ) ( Δθ) ( θ) sin( θ) sin( θ) sin sin cos ng Harber, Lewandowski, McGuirk, & Cornell, PRA n P n id& Ω ΔΩ = t s Δgd it& = u + d + δ gt Ω Ω is& = d + u gs ΔΩ ΔΩ iu& = t + s +Δgu Ω ΔΩ Boson & Fermion Collision hifts Homogeneous Excitations Fermions (p-wave bosons): h Δ ν = m ( a a )( n n ) PP P Bosons (p-wave fermions): h h ν ( a a )( n n ) ( a a a )( n n ) ( Δθ) ( Δθ) ( θ) 4sin( θ) sin( θ) sin sin cos Δ = PP P P PP P m + + sin sin cos ( app + a )( np + n ) Δν Inhomogeneous ( Δθ) ( Δθ) ( θ) 4sin( θ) sin( θ) A number of papers report density shift versus excitation fraction (Rabi pulse). n Harber, Lewandowski, McGuirk, & Cornell, PRA P n KG, PRL 9 /5/3-

6 87 Rb spin-exchange is almost mathematically identical to fermions. Excite dipolar spin waves. ( z) ( δ z...) Ω =Ω + + Optical Clock Fermion Collisions - imulation with Microwave Boson Clock z sin Δ ν = T= ms T= ms T=4 ms T=6 ms T=8 ms T= ms T= ms ( gt ) ( ) cos R cos ωzt Δθ Δθ ( θ R ) TR 4π sin ( θ) sin ( θ) ideband excitations Δν/ 6 N Mean Field..3.4 θ.5,θ (π/) Numerical Analytic Maineult, Deutsch, KG, Reichel, Rosenbusch PRL /5/3- spin waves Position (a.u.) At/cm 3 4,9 3,7 3,,6,,5,,5 increasing density increasing ω ex Time (ms) spin waves - beat ω z and ω ex fit ω ex T R =ms

7 Optical Clock Fermion Collisions - Microwave Boson Clock hift 87 Rb spin-exchange is almost mathematically identical to fermions. Dipolar spin waves. T= ms T= ms T=4 ms T=6 ms T=8 ms T= ms T= ms sin ( gt ) ( ) cos R cos ωzt Δθ Δθ ( θ R ) Δ ν = TR 4π sin ( θ) sin ( θ),5 Differential Collisional Frequency hift (Hz/ At/cm 3 ),5, -,5 -,5 -,75 Experimental Data Analytical solution =,5 Numerical imulation Ramsey time (ms) standard mean-field Maineult, Deutsch, KG, Reichel, Rosenbusch PRL /5/3-3 Observation of Fermion Clock hifts Unique behaviors of Fermion shift, as compared to bosons (Fermion p-waves):. hift Δν is independent of st Ramsey pulse area θ (n n ).. Depends strongly on nd Ramsey pulse θ. not observed for 87 r & 7 Yb p-wave 3. Proportional to s-wave scattering length a. 4. Increases with inhomogeneity as Δθ. 6 Li s-wave Feshbach resonance a (a ) B (G) 4-4 θ θ a =4a Campbell Ye, cience 9 Lemke, Oates, PRL 9 KG, PRL 9 Maineult, Deutsch, KG, Reichel, Rosenbusch, PRL Hazlett, Zhang, tites, KG, O Hara PRL 3

8 Inhomogeneity from Raman beams nuclear spin flip Resolved sideband: ν x,y,z ={3.4, 7, } khz Neglect trap-state changing collisions: λ db à a N / N tot.5 ΔΩ/Ω =.99(6).8(5) 3 t (ms).5(5) 4 6 Li Fermion Clock 75.6 MHz Raman σ + π Raman Raman Beams Beams.6 N /N tot Detuning [ khz ] Hazlett, Zhang, tites, KG, O Hara PRL 3 y z.4. x a (a ) B (G) Raman Beams Dipole Trap Fermion Clock Collision hift. hift Δν is independent of θ (n n ).. Depends strongly on θ. 3. Proportional to a. 4. Increases as Δθ (next). T θ θ g sin Δ sin Δ cos Δ ν = π sin θ sin θ 3 ( θ) ( θ) ( θ) ( ) ( ) θ θ =π/ θ =π/ θ θ = θ θ =π θ θ θ a = 7a == 4a Δν [Hz] θ / π θ / π θ / π θ / π.8 Hazlett, Zhang, tites, KG, O Hara PRL 3

9 Measuring ΔΩ. hift Δν is independent of θ (n n ).. Depends strongly on θ. 3. Proportional to a. 4. Increases as Δθ. Measure Δθ by Rabi flopping and frequency shift of to 3 transition.. Δν/Δν decoh N /N tot.5.5 ΔΩ/Ω =.99(6) RF 3.8(5) 3 t (ms) σ + ΔΩ/Ω =.97() π.98().5. θ Raman /π.5(5) 4 Raman 5.75() θ θ ΔΩ/Ω RFpect. ΔΩ/Ω Rabi a = 4a. Hazlett, Zhang, tites, KG, O Hara PRL 3 pin Waves in Resolved ideband Regime Fermion clock shift spin waves Low vibrational states have high Ω Phase of singlet state evolves through π, and π. Ψ= se iω T ex, { ψψ a b } + t, + u, + d, + { ψψ a b } iωext ( t se ){ ψa ψb } iωext ( t se ){ ψa ψb } = u d { ψψ a b } ρ / ρ a = a a = 7a a = 4a Maineult, Deutsch, KG, Reichel, Rosenbusch, PRL Hazlett, Zhang, tites, KG, O Hara PRL 3

10 Δν/g θ Δ θ = % θ Other Treatments Experimental papers modeling fermions as hδν=μ P μ : Campbell, Ye, cience 9 Lemke, Oates, PRL 9 Blatt, Ye, PRA 9 Theoretical treatments:. All agree on collision shift for Rabi excitation. Physical explanations and viewpoints are different Ramsey KG, PRL 9 Rey, Gorshkov, & Rubbo, PRL 9 Yu & Pethik, PRL θ Ramsey & Rabi Fermions & Bosons inglet-triplet picture Not proportional to n n P. Rabi for Fermions Consistent with n n P & hδν=μ P μ Rabi for Fermions pin precession Consistent with n n P? /5/3-9 trong Interactions More Coherence During Ramsey time, dephasing is a coupling Δ between s & t. ingle state is detuned, g>δ Dephasing becomes off-resonant Rabi flopping elf rephasing spin echo? Contrast revivals occur when singlet gets nπ collisional phase shift. Larger g for tighter traps, including tubes vs. pancakes t u d Ω Δ g ΔΩ s ω ex D D Deutsch, Ramirez-Martinez, Lacroûte LaLoe, Reichel, Rosenbusch, PRL Gibble, Physics Kleine Büning, Will, Ertmer, Rasel, Arlt, Klempt, Rosenbusch, PRL

11 trong Interactions Eliminate hift ingle state is detuned, g>ω Long coherence times for Rb chip traps horter ( st ) Ramsey pulse will excite singlet, longer pulses won t. Eliminate shift by resolving singlet state. Random Ramsey phase (gt >>) gt >> alone doesn t give strong interactions Distribution of g s no shift! How do you prove it? Larger g for tighter traps, including tubes vs. pancakes Im[s(τ )]/dω ΔΩ << Ω π Ω τ. = τ =.T ΔΩ=Ω 5 5g g. KG, Freq Contr. ymp. Discussed in wallows, Ye, Rey, cience, but experiment was r p-wave. Δν (arb.) τ =.5T t u Ω τ = π d s Interferometers - 87 Rb is a boson Fermions or bosons for interferometers? Can particles be identical when their internal states have different momenta? What s the collision shift? Resolved beam splitter diffraction Tight radial confinement - wavepacket in z inglet & Triplet basis Fermions only interact for a short time & P interact for the entire time in a clock Bosons and PP interact the entire time & P only for a short time P z g P t v rec

12 Inhibiting (single particle) Tunneling in μg Resonant tunneling in μg. Accelerated lattice. impler - don t use lattice waist region..g is easy for sites Tunneling is not resonant in accelerated lattices Vertical lattice on earth mg(½λ) =.6 E r Lemonde & Wolf, PRA 5 cattering Induced Tunneling Atoms in adjacent lattice sites have phase shift of ~π. After st scattering, could an atom produce a large frequency shift? Tunneling shift could be n. need a minimum of 3 particles cattering amplitude is not that small. Is shift ε or ε? Ψ ε ε Gibble, PIE /5/3-4

13 cattering Induced Tunneling Consider a double well where only scattering process is allowed. Classical picture atom tunnels and then scatters a lot? Quantum: interference of scattered and unscattered. ε Ψ F Ψ C A V(z) - z Ψ D Ψ B Ψ F Ψ A Ψ B ( θ ) Ψ D Ψ C Ψ A Ψ AΨBΨF ΨAΨCΨD φ sin Δ ν = sin { 4Tε ε sin φ sin θ ( ) ( ) k 3 AF BF k π Ac ( ) ( )} T + ( ε AF + εbf ) 4 ( gac + gad + 4gCD ) ε + gab ( εaf εbf ) sin θ 3 Only ε no interference for amplitude ε. Gibble, PIE /5/3-5 cattering Induced Tunneling What if only the tunneling atom changes state? Then is there interference and a shift proportional to ε? V(z) ε A, ε B J Ψ F Ψ C Ψ F Ψ Ψ A Ψ C Ψ A Ψ B B Ψ A Ψ B - z ΨAΨBΨF ΨAΨBΨC sin ( θ ) φk 3 Δ ν = JTsin ( φk) sin ( θ) + 4TεAFεBF sin sin ( φk) sin ( θ) π Ac T + ( εaf + εbf ) ( gac ( J + εa + εb ) + gbc ( J + εa + εb ) 3 φk + 4g AB ( εa εb ) + ( εaf εbf ) ) sin sin( θ ) Only ε. cattering induced tunneling gives a quadratic density dependence. Order of magnitude is same as for single-particle tunneling. Gibble, PIE /5/3-6

14 ummary First observation of an ultracold collisional frequency shift of a Fermi gas.. hift Δν is independent of θ (n n ).. Depends strongly θ. 3. Increases with inhomogeneity as Δθ. y Applicable to fermion lattice clocks z Can often have smaller Δθ. No trap-state changing collisions & resolved sidebands observed predicted spin waves trong Interactions improve coherence & eliminate shift. Correlations shift Δν= to θ =.5π Max Ramsey fringe contrast biases to colder atoms, giving cos(θ )= at θ =.56π. g correlated with θ lower θ g anti-correlated Δθ higher θ g sin sin cos Δ ν = π sin θ sin θ pairs ( Δθ) ( Δθ) ( θ) ( ) ( ) x θ θ Raman Beams Dipole Trap a = 4a