The a.c. and d.c. Josephson effects in a BEC

Transcription

1 Te a.c. and d.c. osepson effects in a BEC eff Steinauer Saar Levy Elias Laoud Itay Somroni Tecnion - Israel Institute of Tecnology

2 Outline Wat is te a.c. osepson Effect? History Our ultra-ig resolution BEC system Measuring te effect Effects of finite temperature Wat is te d.c. osepson Effect? Measurement of tis effect

3 a.c. osepson Effect B. D. osepson, Pys. Lett., 5 (96). ev ω = a.c. osepson effect is te voltage standard I V microwaves superfluid 3 He S. V. Pereverzev, A. Losak, S. Backaus,. C. Davis, and R. E. Packard, ature 388, 449 (997).

4 Compute te osepson Relations for atoms Ψ, E g g Ψ E i t e : Gross-Pitaevskii equation (T = 0) i Ψ t = m + Vext + g Ψ Ψ no interactions Ψ, E e e Ψg Ψ e Ψ g + Ψ e ω = Ee E g ω depends on te coupling only

5 a.c. osepson Effect B. D. osepson, Pys. Lett., 5 (96). ev ω = a.c. osepson effect is te voltage standard I V microwaves superfluid 3 He S. V. Pereverzev, A. Losak, S. Backaus,. C. Davis, and R. E. Packard, ature 388, 449 (997).

6 Compute te osepson Relations Ψ, E g g Ψ, E e e Ψg Ψ e Ψ g + Ψ Φ ( r ) ( r ) e : Gross-Pitaevskii equation (T = 0) Ψ i = + Vext + g Ψ t m : two-mode approximation Ψ r r Ψ(, t) = ψ ( t) Φ( ) + ψ ( t) Φ Resulting equations iψ& iψ& Φ = r ( ) r = μψ κψ μ ψ 3: write ψ i as ψ κψ i ( ) = e, ψ ( t) t = Te Feynman Lectures e i

7 osepson Relations μ μ ω Assume: + κ / << osepson regime & = & = ω sin Δ μ = ω C & bulk Rigid Pendulum Tese equations are non-linear μ, & μ ψ, ψ,,

8 osepson regime ω measures coupling energy ω measuresinteraction energy C Weak coupling ( ω << ) ω C ω Pase coerence ( ) << C ω Results in: separate condensates ( & = ) Rigid pendulum equations (like superconducting case)

9 Previous interferometers & = ω >> C ω Sin, Y., Saba, M., Pasquini, T. A., Ketterle, W., Pritcard, D. E. & Leanardt, A. E., Pys. Rev. Lett. 9, (004). μ, & μ ψ, ψ,, Scumm, T., Hofferbert, S., Andersson, L. M., Wildermut, S., Grot, S., Bar-osep,I,. Scmiedmayer,. & Krüger, P. ature Pysics, 57-6 (005). Continuous readout Saba, M., Pasquini, T. A., Sanner, C., Sin, Y., Ketterle, W. & Pritcard, D. E. Science 307, (005). osepson regime Albiez, M., Gati, R., Fölling,., Hunsmann, S., Cristiani, M. & Obertaler, M. K. Pys. Rev. Lett. 95, 0040 (005).

10 Our interferometer & = We will observe tis relation by te a.c. osepson effect μ, & μ ψ, ψ,,

11 a.c. osepson Effect μ μ + & = & = ω sin Δ μ = ω C Rigid Pendulum μ, & μ ψ, ψ,, a.c. osepson effect & = const μ & Δ = ω sin t ω =

12 Plasma oscillations μ μ + & = & = ω sin Δ μ = ω C Rigid Pendulum μ, & μ ψ, ψ,, Plasma oscillations π < < π resonance & ω ω = ω C ω

13 Plasma oscillations F. S. Cataliotti, S. Burger, C. Fort, P. Maddaloni, F. Minardi, A. Trombettoni, A. Smerzi, M. Inguscio, Science 93, 843 (00). M. Albiez, R. Gati,. Fölling, S. Hunsmann, M. Cristiani, and M. K. Obertaler, PRL 95, 0040 (005). -D lattice Single BEC osepson junction

14 a.c. osepson Effect μ μ + & = & = ω sin Δ μ = ω C Rigid Pendulum μ, & μ ψ, ψ,, a.c. osepson effect & = const μ & Δ = ω sin t ω =

15 a.c. osepson Effect Internal System D. S. Hall, M. R. Mattews, C. E. Wieman, and E. A. Cornell, PRL 8, 543 (998). -D lattice B. P. Anderson and M. A. Kasevic, Science 8, 686 (998). F =, mf = > F =, mf = - > Δ μ ω = ω C due to asymmetric potential, rater tan population difference Tus, no pendulum equations

16 Tecnion Laboratory M. Greiner, I. Bloc, T. W. Hänsc, and T. Esslinger, Pys. Rev. A 63, 0340(R) (00).

17 Tecnion Laboratory

18 Ultra ig-resolution BEC system probe beam potential beam 4 mm imaging resolution =. μm S. Levy, E. Laoud, I. Somroni, and. Steinauer, ature 449, 579 (007).

19 Ligt barrier Magnetic trapping (Zeeman sift) BEC 0 µm k r Laser ligt seet Electric dipole potential (Stark sift)

20 BEC osepson junction a 5μm b μm S. Levy, E. Laoud, I. Somroni, and. Steinauer, ature 449, 579 (007). /e diameter =.4 μm

21 BEC osepson junction a 5μm

22 Creating = 750 Hz = 450 Hz t (msec) msec Z μ / μ μ p p 0 μm S. Levy, E. Laoud, I. Somroni, and. Steinauer, ature 449, 579 (007).

23 Te a.c. osepson effect 0.8 ω/π (khz) / (khz) Interferometer calibration S. Levy, E. Laoud, I. Somroni, and. Steinauer, ature 449, 579 (007).

24 Effect of te termal atoms (T > 0) μ μ + μ, & μ ψ, ψ,, drives te termal atoms Pendulum & = & = ω sin Δ μ = ω c Damped pendulum & = & = ω sin G Δ μ = ω c I. Zapata, F. Sols, and A.. Leggett, Pys. Rev. A 57, R8 (998).

25 Effect of te termal atoms a.c. osepson effect Pendulum slows down decreases decreases

26 Effect of te termal atoms Pendulum speed Termal fraction = 5% (T 0.3 T c ) t (msec) MQST M. Albiez, R. Gati,. Fölling, S. Hunsmann, M. Cristiani, and M. K. Obertaler, PRL 95, 0040 (005). Macroscopic quantum self-trapping (MQST) Decay of te MQST Termal fraction = 0% (T 0.5 T c ) Damped pendulum & = & = ω sin G Δ μ = ω Interferometer relies on te MQST c S. Levy, E. Laoud, I. Somroni, and. Steinauer, ature 449, 579 (007).

27 d.c. osepson Effect B. D. osepson, Pys. Lett., 5 (96). I Can atoms also do tis? V = 0 Tunneling supercurrent

28 Applying a Current Bias S. Giovanazzi, A. Smerzi, and S. Fantoni, Pys. Rev. Lett. 84, 45 (000). + equil equil > 0 = 0 image & equil is te applied current

29 Applying a Current Bias + Δ μ μ μ μ μ,, ψ,, ψ & μ ω μ Δ = Δ = G sin & & ω μ C = Δ μ ω μ Δ = Δ = G sin & & ( ) C equil ω μ = Δ

30 G Analogous on-linear Systems Δ & μ / ω C ω sin & equil μ μ 0 U & equil equil & <ω = 0 & >ω equil & equil & = & = ω sin G Δ μ = ω ( ) C equil < ω > 0 > ω

31 G Analogous on-linear Systems Δ & μ / ω C ω sin & equil μ μ DC osepson effect & & equil equil < ω = ω sin o 0 U & equil equil & <ω = 0 & >ω equil & equil & = & = ω sin G Δ μ = ω ( ) C equil < ω > 0 > ω

32 -Irelation S. Levy, E. Laoud, I. Somroni, and. Steinauer, ature 449, 579 (007). Wasboard potential 0 U & equil equil & <ω = 0 & >ω equil & equil < ω > 0 > ω Gross-Pitaevskii Equation Image equil DC osepson effect rapid variation time

33 Measured Values ω = 30 sec ω C = = 9000 sec ω << ω C osepson regime Tus, pendulum equations S. Levy, E. Laoud, I. Somroni, and. Steinauer, ature 449, 579 (007).

34 Fluctuations ω effective barrier = = k temperatur e T < B 00 nk 0 μk 0 U & <ω equil & >ω equil ωcω quantum fluctuations = = k B 4 nk Fluctuations are not expected to play a role

35 BEC SQUID detector of rotation Superconducting quantum interference device (SQUID) & equil ω sin Ω ω sin quantization of circulation & max equil = ω cos r mω r A

36 BEC SQUID detector of rotation superfluid 3 He Simmonds, R. W., Marcenkov, A., Hoskinson, E., Davis,. C. & Packard, R. E. ature 4, (00). rapid variation S. Levy, E. Laoud, I. Somroni, and. Steinauer, ature 449, 579 (007).

37 Conclusions We ave made te first observation of te a.c. osepson effect in a single BEC osepson junction We ave made te first observation of te d.c. osepson effect in any atomic system Te MQST is seen to be qualitatively altered by te termal cloud We ave measured te relation between te cemical potential difference and te applied current Te device is suitable for use in te analog of a SQUID detector Tis device constitutes a real-time atom interferometer based on te a.c. osepson effect Tis is te first application of our new type of BEC system wit ultra ig-resolution, capable of applying almost arbitrary potentials and imaging on a tunneling lengt scale

38 Compute te osepson Relations + Δ μ μ μ μ μ,, ψ,, ψ & ψ ψ i i e e = = ω ω μ sin cos = Δ = & & ω μ C = Δ