Supersolid Properties of a Bose-Einstein Condensate in a Ring Resonator

S. C. Schuster, P. Wolf, S. Ostermann, S. Slama, and C. Zimmermann

Phys. Rev. Lett. 124, 143602 – Published 6 April 2020

Abstract

We investigate the dynamics of a Bose-Einstein condensate interacting with two noninterfering and counterpropagating modes of a ring resonator. Superfluid, supersolid, and dynamic phases are identified experimentally and theoretically. The supersolid phase is obtained for sufficiently equal pump strengths for the two modes. In this regime we observe the emergence of a steady state with crystalline order, which spontaneously breaks the continuous translational symmetry of the system. The supersolidity of this state is demonstrated by the conservation of global phase coherence at the superfluid to supersolid phase transition. Above a critical pump asymmetry the system evolves into a dynamic runaway instability commonly known as collective atomic recoil lasing. We present a phase diagram and characterize the individual phases by comparing theoretical predictions with experimental observations.

Received 28 August 2019
Revised 24 October 2019
Accepted 2 March 2020

DOI:https://doi.org/10.1103/PhysRevLett.124.143602

Physics Subject Headings (PhySH)

Atom lasers Atoms, ions, & molecules in cavities Cold gases in optical lattices Collective effects in quantum optics Superradiance & subradiance

Atomic, Molecular & Optical

Authors & Affiliations

S. C. Schuster^1,†, P. Wolf¹, S. Ostermann ^2,*, S. Slama ¹, and C. Zimmermann¹

¹Physikalisches Institut, Eberhard-Karls-Universität Tübingen, Auf der Morgenstelle 14, D-72076 Tübingen, Germany
²Institut für Theoretische Physik, Universität Innsbruck, Technikerstaße 21a, A-6020 Innsbruck, Austria

^*Corresponding author. Stefan.Ostermann@uibk.ac.at
^†simon.schuster@uni-tuebingen.de

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Issue

Vol. 124, Iss. 14 — 10 April 2020

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Images

Figure 1
Experimental setup of a BEC placed in two counterpropagating modes of a ring resonator. The low finesse ${TEM}_{20}$ mode (green, $p$ polarization) and the high finesse ${TEM}_{00}$ mode (red, $s$ polarization) are longitudinally pumped with pump rates $η_{\pm}$ . Both modes are separated in frequency by 160 MHz. The pump power in both modes is monitored with avalanche photodiodes (APDs) by the transmission through one of the resonator mirrors.
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Figure 2
Phase diagram presented as a plot of the total kinetic energy $E_{kin}$ of the BEC after an interaction time $τ = 1 ms$ . To increase the contrast at the CARL phase boundary, the colorbar is truncated for values with $E_{kin} > 3$ . We find three fundamentally different phases: the superfluid phase where the BEC has a homogeneous density distribution (to the left of the dashed yellow line), a supersolid phase (to the right of the dashed yellow and below the solid blue line), and a CARL regime (above the solid blue line). The white lines show the phase boundaries extracted from the experimental data for the superfluid to supersolid and CARL (white dotted line) phase transition. The grey squares mark parameter sets without data.
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Figure 3
Exemplary time evolutions in the CARL and the supersolid regime. The first row (a)–(c) shows the dynamics in the CARL regime for $(| A | / S, S) = (0.95, 6.32)$ . The measured evolution of the populated momentum states $| c_{n} |^{2}$ with $n = 0, + 2, + 4$ (black, red, green) (a) are in good agreement with the numerical simulations (b). The numerically obtained time evolution of the spatial distribution of the BEC exhibits a strong acceleration along the $+ x$ direction (c). In the second row (d)–(f) a typical time evolution leading to a stable supersolid state is shown for $(| A | / S, S) = (0.008, 8.15)$ . (d) Measured time evolution of $| c_{n} |^{2}$ for $n = - 2, 0, + 2$ (blue, black, red). (e) and (f) corresponding numerical time evolution. The error bars in (a) and (d) are the standard deviation of the mean value of each data point. Note that we only show momentum components with nonzero values during the time evolution.
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Figure 4
Reversibility and phase coherence of the excited crystalline structure for $(| A | / S, S) = (0.06, 8.2)$ . In (a) the evolution of single momentum states $n = - 2$ , 0, 2 (blue, black, red) is presented together with the exemplary progression of both pump powers (grey), while ramps are applied. (b)–(d) show the average of eight TOF pictures for pump times (b) $t < 0.2 ms$ , (c) $0.5 ms < t < 1 ms$ and (d) $t > 1.5 ms$ . The TOF pictures are scaled alike.
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