Realization of a Periodically Driven Open Three-Level Dicke Model

Phatthamon Kongkhambut, Hans Keßler, Jim Skulte, Ludwig Mathey, Jayson G. Cosme, and Andreas Hemmerich

Phys. Rev. Lett. 127, 253601 – Published 13 December 2021

Abstract

A periodically driven open three-level Dicke model is realized by resonantly shaking the pump field in an atom-cavity system. As an unambiguous signature, we demonstrate the emergence of a dynamical phase, in which the atoms periodically localize between the antinodes of the pump lattice, associated with an oscillating net momentum along the pump axis. We observe this dynamical phase through the periodic switching of the relative phase between the pump and cavity fields at a small fraction of the driving frequency, suggesting that it exhibits a time crystalline character.

Received 26 August 2021
Accepted 2 November 2021

DOI:https://doi.org/10.1103/PhysRevLett.127.253601

Physics Subject Headings (PhySH)

Bose-Einstein condensates Cavity quantum electrodynamics Cold gases in optical lattices

Atomic, Molecular & Optical

Authors & Affiliations

Phatthamon Kongkhambut¹, Hans Keßler ^1,*, Jim Skulte ^1,2, Ludwig Mathey^1,2, Jayson G. Cosme ³, and Andreas Hemmerich ^1,2

¹Zentrum für Optische Quantentechnologien and Institut für Laser-Physik, Universität Hamburg, 22761 Hamburg, Germany
²The Hamburg Center for Ultrafast Imaging, Luruper Chaussee 149, 22761 Hamburg, Germany
³National Institute of Physics, University of the Philippines, Diliman, Quezon City 1101, Philippines

^*Corresponding author. hkessler@physnet.uni-hamburg.de

Parametrically driven dissipative three-level Dicke model

Jim Skulte, Phatthamon Kongkhambut, Hans Keßler, Andreas Hemmerich, Ludwig Mathey, and Jayson G. Cosme

Phys. Rev. A 104, 063705 (2021)

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Vol. 127, Iss. 25 — 17 December 2021

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Images

Figure 1
(a) Schematic of the transversely pumped and shaken atom-cavity system. A sample of cold atoms is placed in a cavity oriented along the $z$ axis. A standing wave potential is periodically shifted along the $y$ axis using phase modulation techniques. (b) Dynamical phase diagram with two distinct regions: In the red area, the dynamics of the system is captured by a two-level Dicke model. In the blue area, a three-level Dicke model is required. (c) Dynamics of the product of the relevant order parameters for strong driving in the three-level Dicke regime (blue) and for weak driving in the two-level Dicke regime (red). The modulation frequency is $ω_{dr} / 2 π = 9.4 kHz$ and $ω_{B} / 2 π = 8 kHz$ .
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Figure 2
Single-shot realization of DBDW order. (a) Time sequence for the pump lattice depth (blue) and the phase $ϕ$ of the pump field (red) with modulation strength $f_{0} = 0.1 π$ and a modulation frequency $ω_{dr} = 11.5 kHz$ . (b) Phase difference $φ$ between the pump and intracavity field (green trace) and photon number $N_{P}$ in the cavity (red trace). The dashed vertical lines mark the time interval during which the modulation strength is increased. The gray shaded area shows the time window for the close-up presented in (c). (c) The red trace repeats the intracavity photon number $N_{P}$ from (b). The blue data points plot the product $Θ_{DW} \times Θ_{BDW}$ , approximately given by $Δ \tilde{F}$ [see also Fig. 1]. Each data point is averaged over five realizations. The solid line shows a fit with a product of two harmonic oscillations. (d)–(h) Single-shot momentum distributions recorded at the times marked in (c).
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Figure 3
(a) $ω_{DW}$ is plotted against $ω_{dr}$ . $ω_{DW}$ is extracted by the position of a Gaussian fit of the amplitude spectrum calculated from the measured time evolution of the phase difference between the pump and cavity fields $φ$ . Each data point is averaged over hundreds of realizations with different modulation strength $f_{0}$ and fixed $ω_{dr}$ . The gray line is a linear fit yielding the result shown in the plot legend. (b) The relative crystalline fraction $Ξ$ is plotted as a function of the modulation frequency $ω_{dr}$ and strength $f_{0}$ . The diagram is constructed by dividing the parameter space into $20 \times 16$ plaquettes and averaging over multiple experimental runs within each.
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Figure 4
Dynamics in the three-level Dicke regime using an initial homogeneous BEC state. (a) Time sequence for the pump lattice depth (blue) and the phase $ϕ$ of the pump field (red) with modulation strength $f_{0} = 0.1 π$ and a modulation frequency $ω_{dr} = 11.5 kHz$ . (b) The phase difference $φ$ between the pump and intracavity field is plotted in green and the photon number $N_{P}$ in the cavity in red.
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