How to exploit driving and dissipation to stabilize and manipulate quantum many-body states

TL;DR

The paper surveys driven-dissipative quantum fluids of light, detailing how external pumping and losses transform standard many-body physics into a controllable non-equilibrium setting. It builds a theoretical framework combining conservative photon dynamics with open-system methods, including mean-field Gross-Pitaevskii-type equations and beyond, to describe both weakly and strongly interacting regimes. Concrete realizations include coherent pumping of homogeneous and topologically nontrivial photonic lattices, observation of analog horizons and IQH physics, and strategies to stabilize FQH-like states via frequency-selective incoherent pumping, highlighting both fundamental insights and experimental prospects. Overall, the work points to rich opportunities at the interface of quantum optics, many-body physics, and analog gravity, with potential applications in quantum simulation and photonic quantum technologies.

Abstract

We review the basic concepts of quantum fluids of light and the different techniques that have been developed to exploit driving and dissipation to stabilize and manipulate interesting many-body states. In the weakly interacting regime, this approach has allowed to study, among other, superfluid light, non-equilibrium Bose-Einstein condensation, photonic analogs of Hall effects, and is opening the way towards the realization of a new family of analog models of gravity. In the strongly interacting regime, the recent observations of Mott insulators and baby Laughlin fluids of light open promising avenues towards the study of novel strongly correlated many-body states.

Figures (6)

• Figure 1: Light confinement in a planar microcavity (top) results in a relativistic dispersion for the in-plane motion of photons (bottom left). Feynman diagram describing the Heisenberg-Euler photon-photon interaction processes mediated by virtual electron-positron pairs in Quantum Electrodynamics (bottom right).
• Figure 2: Left panels: plot of the equation of state of the fluid of light, expressed as fluid density as a function of pump intensity for two different incident frequencies in respectively the optical limiter regime (top) and the bistable regime (bottom). The dashed line indicates the dynamically unstable regions. Right panel: Real part (top) and imaginary part (bottom) of the excitation frequencies for the nonequilibrium Bogoliubov modes corresponding to the points indicated as A, B', C, C', D, E in the left panel.
• Figure 3: Left (a-b) panels: color plots of the numerically calculated steady-state intensity distribution in a coherently pumped $q=5$ photonic Harper-Hofstadter model. The pump is localized on the central site and is resonant with the lowest photonic band. The loss rate is taken to be larger than the bandwidth $\gamma_{\rm loss}/ \Delta\omega_{\rm band}=2$, so to be in the IQH regime. In the upper (a) panel, no external force is present and the distribution has a $\pi/2$ rotational symmetry. In the lower (b) panel, a force along the negative $y$ direction is applied, and the intensity distribution moves leftwards along the transverse $x$ direction. The magnitude of this displacement agrees with the prediction of the driven-dissipative IQH formula \ref{['eq:transverse_shift_quantized']}. Right panel: for a loss rate smaller than the bandwidth $\gamma_{\rm loss}/\Delta\omega_{\rm band}\simeq 1/30$ of the lowest band of a $q=3$ Harper-Hofstadter, we are in the anomalous quantum Hall regime and the displacement is determined by the average of the Berry curvature over all states resonant with the pump frequency $\omega_{\rm inc}$. Within a photonic band (white region), the value of the Berry curvature extracted from the numerically calculated transverse shift (green points) are successfully compared to the value of the Berry curvature extracted from the Harper-Hofstadter band structure. Panels adapted from Ozawa:PRL2014.
• Figure 4: Left panels: plot of the real (a) and imaginary (b) parts of the dispersion of the collective excitations of a non-equilibrium condensate under incoherent pumping at $P/\gamma_{\rm loss}=2$. For small $k$ values, the dispersion displays a diffusive behaviour with a zero real part and a quadratically growing imaginary part. Right (c-h) panels: generalized Landau criterion for non-equilibrium condensates. Panels (c-e) show the density perturbation induced in a fluid moving in the positive $x$ direction by an impurity at rest. The different panels refer to different values of the condensate velocity $v/c_s =1.5, 1, 0.4$ across the (equilibrium) speed of sound $c_s=\sqrt{g_{\rm nl}\,|\psi|^2/m}$. Panel (f) shows the (normalized) force exerted by the fluid on the defect as a function of the condensate velocity $v/c_s$ for different values of the non-equilibrium parameter $\gamma_{\rm loss}/g_{\rm nl}\,|\psi|^2=0,\,0.1,\,1,\,2$. For the smallest $\gamma_{\rm loss}$ values, the sudden onset of friction that is visible in the vicinity of the critical speed $v/c_s= 1$ is a non-equilibrium counterpart of the Landau critical velocity of equilibrium superfluids pitaevskii2016bose. Panels (g-h) show a cut of the real and the imaginary part of the wavevector of the collective excitations emitted in the negative $x$ direction as a function of the speed for an intermediate loss case with $\gamma_{\rm loss}/g_{\rm nl}\,|\psi|^2=1$. The sudden onset of friction in (f) corresponds to the singular point that is visible in (g-h) slightly below $v/c_s= 1$. Panels (c-h) are adapted from Wouters:PRL2010.
• Figure 5: Left panel (a): sketch of the photon blockade mechanism for a single-mode cavity under a coherent pumping exactly on resonance with the bare cavity frequency, $\omega_L=\omega_o$. Because of the strong nonlinearity $\omega_{\rm nl}\gg \gamma_{\rm loss}$, transitions to all $N>1$ states are non-resonant and the dynamics is confined to the $N=0,1$ states, giving effectively impenetrable photons. Central panel (b): sketch of the coherent pumping scheme to selectively excite a $N=3$-photon state via a three-photon transition. Top-right panel: generation of a Tonks-Girardeau gas of fermionized photons under coherent pumping. Spectrum of total photon number $n_T$ as a function of the incident frequency $\Delta\omega_p=\omega_{\rm inc}-\omega_o$ for different values of the pump intensity, $F/\gamma_{\rm loss}=0.1,\,0.3,\,1,\,2,\,3$. Photons are assumed to be perfectly impenetrable $U/\gamma_{\rm loss}=\infty$ and $J/\gamma_{\rm loss}=20$. For each many-body state, the vertical dotted lines indicate the theoretical prediction for the position of the $N$-photon resonance peak; the label indicates the orbitals filled in the corresponding fermionic wavefunction. Bottom-right panel: second order photon correlations in the emission from the same (black) and from different (red) sites as a function of the interaction constant $\omega_{\rm nl}/\gamma_{\rm loss}$. At each point, the coherent drive is set on resonance with the lowest two-photon state of a 3-sites chain. The right panels are adapted from Carusotto:PRL2009.