Meissner-like Effect for a Synthetic Gauge Field in Multimode Cavity QED

Kyle E. Ballantine, Benjamin L. Lev, and Jonathan Keeling

Phys. Rev. Lett. 118, 045302 – Published 27 January 2017

Abstract

Previous realizations of synthetic gauge fields for ultracold atoms do not allow the spatial profile of the field to evolve freely. We propose a scheme which overcomes this restriction by using the light in a multimode cavity with many nearly degenerate transverse modes, in conjunction with Raman coupling, to realize an artificial magnetic field which acts on a Bose-Einstein condensate of neutral atoms. We describe the evolution of such a system and present the results of numerical simulations which show dynamical coupling between the effective field and the matter on which it acts. Crucially, the freedom of the spatial profile of the field is sufficient to realize a close analogue of the Meissner effect, where the magnetic field is expelled from the superfluid. This backaction of the atoms on the synthetic field distinguishes the Meissner-like effect described here from the Hess-Fairbank suppression of rotation in a neutral superfluid observed elsewhere.

Received 25 August 2016

DOI:https://doi.org/10.1103/PhysRevLett.118.045302

Physics Subject Headings (PhySH)

Atoms, ions, & molecules in cavities Cavity quantum electrodynamics Meissner effect Superfluidity Synthetic gauge fields

Bose-Einstein condensates Ultracold gases

Atomic, Molecular & OpticalCondensed Matter, Materials & Applied Physics

Authors & Affiliations

Kyle E. Ballantine¹, Benjamin L. Lev², and Jonathan Keeling¹

¹SUPA, School of Physics and Astronomy, University of St. Andrews, St. Andrews KY16 9SS, United Kingdom
²Departments of Physics and Applied Physics and Ginzton Laboratory, Stanford University, Stanford, California 94305, USA

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Vol. 118, Iss. 4 — 27 January 2017

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Figure 1
(a) A 2D Bose-Einstein condensate (BEC) is coupled to linearly polarized counterpropagating Raman beams in $\hat{x}$ and trapped inside a cavity set in the multimode, confocal configuration. (Optical trapping lasers are not shown, and only ${TEM}_{10}$ and ${TEM}_{01}$ modes are shown for simplicity.) The axis of the oblate BEC is collinear with the cavity axis. The cavity, with field loss $κ$ , is pumped along $+ \hat{z}$ by a circularly polarized field of frequency $ω_{p}$ detuned by $Δ_{0}$ from the confocal cavity frequency $ω_{0}$ . The pump laser is spatially shaped with a digital multimirror device (DMD) spatial light modulator before cavity injection. Cavity light is imaged by an EMCCD camera. (The atomic absorption imaging laser and camera are not shown.) A magnetic field $B$ is oriented along $+ \hat{z}$ . (b) ${}^{87}{Rb}$ atomic level diagram with three coupling lasers shown. Green arrows show the pump field that Stark shifts the state $| A ⟩$ and $| B ⟩$ by $E_{A, B}$ . The laser frequency is set to the tune-out wavelength between the $D_{1}$ and $D_{2}$ lines in ${}^{87}{Rb}$ . The blue arrows show the two-photon Raman-coupling fields driving $π$ and $σ_{-}$ transitions—effected by obeying electric dipole selection rules for the polarizations given in (a)—with Rabi frequencies $Ω_{i}$ . The Raman fields are detuned from $ω_{0}$ by a quarter of a free spectral range $Δ_{FSR} / 4$ and the $m = 0$ state is detuned by $ε$ via the quadratic Zeeman shift.
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Figure 2
(a) Ground state of the condensate in a static field $| φ |^{2} \propto | y |$ showing vortex formation. (b) Density of the condensate when the field is allowed to evolve. No vortices remain in the cloud. (c) Relative intensity (i.e., $| φ |^{2} / | f_{0} |^{2}$ ) of light in a cavity with no atom-light coupling used to generate (a). (d) Steady-state relative intensity of light when coupled to an atomic cloud, showing a reduction in the region where atoms are present. Vortices remain in the region of low atomic density where the intensity recovers and so the magnetic field is high. (e) Applied magnetic field [derivative of the intensity in (c)] and (f) magnetic field after coupled evolution showing the applied field has been expelled from the condensate. All lengths are in units of the harmonic oscillator length $a_{0} = 1 / \sqrt{m ω_{x}}$ . Using $ω_{x}$ as the frequency unit, other parameters are given by $δ = - 10$ , $l = 1$ , $Δ_{0} = - 50$ , $κ = 1000$ , $E_{Δ} = 50$ , $q = 70$ , $Ω = 1 0^{5}$ , $m U = 1.5 \times 10^{- 3}$ , $N = 1 0^{6}$ , and $f_{0} = 4$ , all relevant for the cavity considered in Refs. [53, 54].
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Figure 3
Profile of the (a) atomic density and (b) artificial field with varying numbers of atoms, in terms of the dimensionless parameter $m N U$ . For realistic values, this corresponds to $N = 1 0^{5}$ (blue curve), $N = 5 \times 1 0^{5}$ (yellow curve), $N = 1 0^{6}$ (green curve), and $N = 5 \times 1 0^{6}$ (orange curve). All other parameters are the same as in Fig. 2.
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