Condensate Formation in a Dark State of a Driven Atom-Cavity System

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

Phys. Rev. Lett. 130, 163603 – Published 21 April 2023

Abstract

We demonstrate the formation of a condensate in a dark state of momentum states, in a pumped and shaken cavity-BEC system. The system consists of an ultracold quantum gas in a high-finesse cavity, which is pumped transversely by a phase-modulated laser. This phase-modulated pumping couples the atomic ground state to a superposition of excited momentum states, which decouples from the cavity field. We demonstrate how to achieve condensation in this state, supported by time-of-flight and photon emission measurements. With this, we show that the dark state concept provides a general approach to efficiently prepare complex many-body states in an open quantum system.

Received 6 September 2022
Accepted 14 March 2023

DOI:https://doi.org/10.1103/PhysRevLett.130.163603

Physics Subject Headings (PhySH)

Bose-Einstein condensates Cavity quantum electrodynamics

Atomic gases Bose gases

Atomic, Molecular & Optical

Authors & Affiliations

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

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

^*These authors contributed equally to this work.

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Vol. 130, Iss. 16 — 21 April 2023

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Images

Figure 1
(a) Sketch of the experimental setup. An electro-optical modulator (EOM) is used to modulate the phase of the pump field, which results in shaking the pump potential. The light leaking out the cavity is detected using a photo diode (PD). (b) Sketch of the momentum distribution of the three relevant superpositions of momentum modes, the normal state $| N ⟩$ , the bright state $| B ⟩$ , and the dark state $| D ⟩$ , which form a three-level Dicke model shown in (c) with the atom-cavity coupling $λ$ and the shaking-induced functions $h_{1} (t)$ and $g_{1} (t)$ . The colors in (b) represent the phase of the momentum states, where blue indicates a phase shift of $π$ relative to red.
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Figure 2
(a),(b) Population of the dark state for different driving frequencies $ω_{dr}$ and driving strengths $f_{0, theory}$ . The driving frequency axis is rescaled by the characteristic frequency of the dark state $ω_{D}$ . (a) The results from the three-level model and (b) the full atom-cavity simulation. The phase diagrams are constructed for 7 driving cycles.
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Figure 3
(a) Simulations of the evolution of the three highest eigenvalues of the single-particle correlation function are shown. Gray dashed and solid vertical lines denote, respectively, the times when the snapshots of the single-particle densities in (b) and (c) are taken. The real-space densities in (b) and (c) are color coded to show the phase of $Ψ (y, z)$ . (d),(e) Evolution of the occupations of $| N ⟩$ , $| B ⟩$ , and $| D ⟩$ , while the pump is adiabatically ramped down. Panels (d) and (e), respectively, correspond to initial conditions according to the dashed and solid gray vertical lines in (a).
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Figure 4
Experimental phase diagram of the population of the dark state for different driving frequencies $ω_{dr}$ and driving strengths $f_{0, \exp}$ . The driving frequency axis is rescaled by the characteristic frequency of the dark state $ω_{D}$ . The phase diagram is constructed for 6 driving cycles. (b)–(d) Population of the dark state as a function of the driving cycles for the parameter sets marked by a diamond, a circle, and a rectangle in (a). The population of the dark state is rescaled by the total particle number $N_{a}$ for different driving cycles derived from time-of-flight (TOF) images in (b)–(d). Examples of TOF images are provided before shaking starts at $t = 0$ (e) and after around 6 driving cycles (f). All TOF images are obtained after an adiabatic ramp-down of the pump wave and ballistic expansion of 25 ms. (g) Time sequence for the pump strength (red) and the phase $ϕ$ of the pump field (blue). (h) Phase difference $φ$ between the pump and intracavity field (blue) and intracavity photon number $N_{P}$ (red) for the driving parameters marked by a circle in (a).
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