Interaction-Induced Quantum Phase Revivals and Evidence for the Transition to the Quantum Chaotic Regime in 1D Atomic Bloch Oscillations

F. Meinert, M. J. Mark, E. Kirilov, K. Lauber, P. Weinmann, M. Gröbner, and H.-C. Nägerl

Phys. Rev. Lett. 112, 193003 – Published 15 May 2014

Abstract

We study atomic Bloch oscillations in an ensemble of one-dimensional tilted superfluids in the Bose-Hubbard regime. For large values of the tilt, we observe interaction-induced coherent decay and matter-wave quantum phase revivals of the Bloch oscillating ensemble. We analyze the revival period dependence on interactions by means of a Feshbach resonance. When reducing the value of the tilt, we observe the disappearance of the quasiperiodic phase revival signature towards an irreversible decay of Bloch oscillations, indicating the transition from regular to quantum chaotic dynamics.

Received 16 September 2013

DOI:https://doi.org/10.1103/PhysRevLett.112.193003

Authors & Affiliations

F. Meinert¹, M. J. Mark¹, E. Kirilov¹, K. Lauber¹, P. Weinmann¹, M. Gröbner¹, and H.-C. Nägerl¹

¹Institut für Experimentalphysik und Zentrum für Quantenphysik, Universität Innsbruck, 6020 Innsbruck, Austria

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Vol. 112, Iss. 19 — 16 May 2014

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Images

Figure 1
Interaction-induced collapse and revival of atomic Bloch oscillations in a large ensemble of 1D tubes. The lattice depth along the tubes is $V_{z} = 7 E_{R}$ ( $J = 52.3 Hz$ ). Time-of-flight absorption images of one Bloch cycle are shown after $t_{h} = 0$ , 7, 14 $T_{B}$ for zero interaction (a–c) and for $a_{s} = 21.4 (1.5) a_{0}$ (e–g), respectively. The vertical bar in (a) indicates the extent of the first Brillouin zone. Full time evolution of the mean atomic momentum is shown for zero interaction (d) and for $a_{s} = 21.4 (1.5) a_{0}$ (h). Solid lines are fits to the data using the analytic model function (see text). The shaded areas indicate the data points shown in the time-of-flight pictures.
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Figure 2
Dependence of the revival frequency $f_{rev}$ on the on-site interaction energy $U$ . (a) Extracted $f_{rev}$ (circles) and Bloch frequency $f_{B}$ (triangles) from model fits of Eq. (2) to time traces $⟨ p ⟩ (t_{h})$ as shown in Fig. 1 as a function of $a_{s}$ . Error bars are smaller than the data points. The shaded gray area depicts the calculated $U$ , taking into account a 5% error on the lattice depth. The solid line denotes a constant fit to the data for $f_{B}$ . Mean atomic momentum as a function of hold time for $a_{s} = 40.6 (1.5) a_{0}$ (b), giving $U = 194 (10) Hz$ , and $a_{s} = 111.5 (1.5) a_{0}$ (c), giving a comparatively large $U = 533 (15) Hz$ . Solid lines are fits to the data based on Eq. (2).
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Figure 3
Transition from regular to chaotic dynamics when varying the tilt $E$ . (a) Mean atomic momentum as a function of hold time for $E = 855 (15) Hz$ (triangles) and $E = 266 (5) Hz$ (squares) at $a_{s} = 26.9 (1.5) a_{0}$ . Here, $V_{z} = 4 E_{R}$ ( $J = 114.2 Hz$ ), giving $U = 106 (8) Hz$ . Solid lines show fits to the data based on the analytic model function, Eq. (2), in the strong-forcing limit and an exponentially damped sinusoidal in the chaotic regime. The two data sets are offset for clarity. Bloch frequency $f_{B}$ (b) and exponential decay time $τ$ (c) as a function of $E$ (circles) extracted from exponentially damped sinusoidal fits to the initial decay in data sets as depicted in (a). Triangles in (c) depict the amplitude of the revival $δ p$ as a function of $E$ . The dashed line in (b) is a linear fit to the data. The dashed lines in (c) are error-function fits to the data to guide the eye. The shaded areas indicate the prediction from numerical simulations with $1 \leq n \leq 1.4$ [27].
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Figure 4
Dependence of the irreversible decay of Bloch oscillations on atom-atom interactions in the chaotic regime. (a) Mean atomic momentum as a function of hold time for $a_{s} = 4.5 (1.5) a_{0}$ (squares), $a_{s} = 20.8 (1.5) a_{0}$ (triangles), and $a_{s} = 83.4 (1.5) a_{0}$ (circles) at $E = 346 (10) Hz$ . Here, $V_{z} = 4 E_{R}$ ( $J = 114.2 Hz$ ). Solid lines are exponentially damped sinusoidal fits to the data. (b) Exponential decay rate $1 / τ$ as a function of $a_{s}$ extracted from data sets, as shown in (a). The dashed line shows a prediction from numerical simulations for a homogeneous system without a trap.
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