Non-equilibrium Josephson Oscillations of Trapped Bose-Einstein Condensates

Transcription

1 Universität Konstanz Non-equilibrium Josephson Oscillations of Trapped Bose-Einstein Condensates Johann Kroha 1 Collaborators: Mauricio Trujillo Martinez 1 Anna Posazhennikova 2 1 Institute of Physics, University of Bonn, Germany 2 Department of Physics, University of Konstanz, Germany M. Truillo Martinez, A. Posazhennikova, J. Kroha, PRL 103, (2009) INES Winter School, IISER Mohanpur, 11 January, 2012

2 Motivation Measurement of the quantum phase Merging of two Bose condensates in a double-well potential non-adiabatic Josephson oscillations and damping With repulsive interaction: Initial state energy + >> merge ground state energy of merged system Thermalization in final state? Where do entropy and energy go (isolated system)? Time scale(s)? Bogoliubov quasiparticle excitations Experiments by Oberthaler Thywissen groups

3 Introduction: Josephson effect in bulk systems Particle current oscillations between two weakly coupled, macroscopic, coherent quantum systems B. D. Josephson, 1962 I = Icsin( θ ) SC I SC DC const Conditions: 1) well defined quantum phase (grand canonical ensemble) 2) weak coupling AC θ t = Δμ = 2eΔV

4 ose Josephson junction: theory Cold bosonic gas in a double-well potential Microscopic (quantum) Hamiltonian: V ext Dilute and cold systems: contact interaction: a s : scattering length

5 Bose Josephson junction: 2-mode approximation Classical Josephson Hamilton function H / J = 2 n 2 + En 1 n 2 cos relative population imbalance n= N 1 N 2 N tot phase difference interaction parameter: (inverse mass) = UN tot 2J Smerzi et al., PRL 79, 4690 (1997)

6 Josephson oscillations in a double-well Bose Josephson Junction: theory Josephson frequency: Smerzi et al., PRL 79, 4690 (1997) J 2 J 1 NtotU 2J c self-trapping: rotating pendulum AC Josephson delocalized: small-amplitude oscillations

7 Bose junction: experiment Josephson oscillations: Experiment M. Albiez,, M. Oberthaler et al., PRL 95, (2005); Thywissen et al. (2010)

8 Josephson oscillations: experiment Phase space portrait self-trapped (AC Josephson) delocalized (DC Josephson) M. Albiez,, M. Oberthaler et al., PRL 95, (2005); Thywissen et al. (2010)

9 Bose Josephson junction out of equilibrium Instantaneous switching on the Josephson coupling J( t) J ( t) Coupling to Bogoliubov quasiparticle excitations

10 Bose Josephson junction out of equilibrium Bogoliubov quasiparticles out of single-particle states of the trap Classical condensate amplitudes: Bose field operators for excitations:

11 BEC + quasiparticle quantum Hamiltonian

12 ose-josephson junction out of equilibrium Equations of motion: Keldysh Quasiparticles (Hartree-Fock selfenergies) Condensates M. Truillo Martinez, A. Posazhennikova, J. Kroha, PRL 103, (2009)

13 Parameter regimes: quasiparticle level spacing Josephson oscillation is a periodic perturbation for qp subsystem: J J : : quasiparticles effectively not excited in low order PT. perturbative excitation of quasiparticles: golden rule damping. c small traps, large large (non-perturbative) e.g. experiments of M. Oberthaler et al. vs c large traps, small finite (golden rule) e.g. experiments of J. Thywissen et al. (private communication) undamped oscillations (relaxation??) oscillations quickly damped

14 ose Josephson junction out of equilibrium Results: initially delocalized J : population imbalance quasiparticle occupation number population imbalance phase difference (5 levels) M. Truillo Martinez, A. Posazhennikova, J. Kroha, PRL 103,, (2009)

15 ose Josephson junction out of equilibrium Results: initially self-trapped population imbalance quasiparticle occupation number population imbalance phase difference (5 levels)

16 ose-josephson junction out of equilibrium Results: phase diagram and scaling J -K scaling

17 Outlook: time scales for equilibration + - merge = T : Characteristic time scales: Destruction of Josephson oscillations: Quasiparticle damping: Thermalization of quasiparticles + BEC: c qp therm

18 ose-josephson junction out of equilibrium Conclusions and outlook Dynamics of coupled BECs including Bogoliubov excitations: non-equilibrium Josephson oscillations Characteristic time scales (non-exponential): Destruction of Josephson oscillations: Quasiparticle damping: Thermalization of quasiparticles + BEC: c qp therm (in progress) Relation to inflation in the early universe? Strong damping of Josephson oscillations only in large traps: J :