[Paper Review] Dynamics and phase evolution of Bose-Einstein condensates in one-dimensional optical lattices

O. Morsch, Matteo Cristiani+3 more|arXiv (Cornell University)|Sep 2, 2002

Cold Atom Physics and Bose-Einstein Condensates3 citations

TL;DR

This study investigates the dynamics and phase evolution of Bose-Einstein condensates (BECs) in one-dimensional optical lattices using adiabatic loading and non-adiabatic switching of the lattice potential. Key findings include the observation of visibility decay and revival in interference patterns due to phase decoherence and tunneling, with revival induced by reducing lattice depth, demonstrating coherent tunneling and re-thermalization dynamics in trapped ultracold atoms.

ABSTRACT

We report experimental results on the dynamics and phase evolution of Bose-Einstein condensates in 1D optical lattices. The dynamical behaviour is studied by adiabatically loading the condensate into the lattice and subsequently switching off the magnetic trap. In this case, the condensate is free to expand inside the periodic structure of the optical lattice. The phase evolution of the condensate, on the other hand, can be studied by non-adiabatically switching on the periodic potential. We observe decays and revivals of the interference pattern after a time-of-flight.

Motivation & Objective

• To investigate the dynamical expansion of BECs in stationary 1D optical lattices after adiabatic loading and magnetic trap release.
• To study the phase evolution of BECs when the optical lattice is switched on non-adiabatically, focusing on coherence and interference pattern evolution.
• To characterize the role of tunneling, effective mass, and thermalization in the coherence and expansion dynamics of BECs in periodic potentials.
• To quantify the visibility of interference patterns as a measure of phase coherence between lattice sites over time.
• To explore the interplay between tunneling, radial oscillations, and re-thermalization in non-adiabatic lattice loading.

Proposed method

• Adiabatically loaded a BEC of 87 Rb atoms into a 1D optical lattice by ramping up the lattice depth over 150 ms, ensuring adiabaticity for chemical potentials above 50 Hz.
• Imaged the time-of-flight expansion of the BEC after switching off the magnetic trap to study free expansion dynamics along and perpendicular to the lattice direction.
• Used a modified Gross-Pitaevskii approach with an effective mass m*(U₀) derived from band structure calculations to model expansion in the lattice direction.
• Measured the perpendicular expansion to infer the chemical potential of the BEC in the lattice as a function of lattice depth.
• Non-adiabatically switched on the lattice to study phase evolution, observing interference pattern visibility decay and revival over time.
• Quantified phase coherence via visibility ξ = (h_peak - h_middle)/(h_peak + h_middle), tracking its temporal evolution to assess coherence between lattice sites.

Experimental results

Research questions

• RQ1 How does the expansion of a BEC in a 1D optical lattice depend on lattice depth and effective mass?
• RQ2 What causes the initial decay and subsequent revival of interference pattern visibility after non-adiabatic lattice loading?
• RQ3 To what extent does tunneling between lattice sites drive the revival of phase coherence in the BEC?
• RQ4 How do radial oscillations and re-thermalization affect the phase coherence and visibility evolution in the BEC?
• RQ5 What is the role of the non-condensed fraction in the observed coherence dynamics and energy redistribution?

Key findings

• The condensate exhibited suppressed expansion along the lattice direction due to localization in individual lattice wells, while perpendicular expansion increased due to higher chemical potential upon lattice loading.
• Theoretical modeling using an effective mass and variable chemical potential accurately reproduced the perpendicular expansion dynamics, corrected for imaging resolution.
• Visibility ξ initially decayed from ~0.6–0.9 to near zero within 5–20 ms, depending on trap frequency, indicating rapid dephasing of lattice-site wavefunctions.
• For trap frequencies >30 Hz, visibility revived and fluctuated before stabilizing near the initial value, indicating coherent re-establishment of phase through tunneling and energy redistribution.
• For weak traps (<30 Hz), visibility remained near zero for up to 200 ms, but could be revived by reducing lattice depth to ~4 E_rec, confirming tunneling’s role in coherence recovery.
• The revival of visibility upon depth reduction demonstrates that tunneling between sites is essential for phase coherence recovery, with re-thermalization occurring on a timescale comparable to radial oscillation damping and revival dynamics.