Superradiant Phase Transition in Electronic Systems and Emergent Topological Phases

Quantum Phase Transitions in Optomechanical Systems

In this Letter, we investigate the ground state properties of an optomechanical system consisting of a coupled cavity and mechanical modes. An exact solution is given when the ratio η between the cavity and mechanical frequencies tends to infinity. This solution reveals a coherent photon occupation in the ground state by breaking continuous or discrete symmetries, exhibiting an equilibrium quantum phase transition (QPT). In the U(1)-broken phase, an unstable Goldstone mode can be excited. In the model featuring Z_{2} symmetry, we discover the mutually (in the finite η) or unidirectionally (in η→∞) dependent relation between the squeezed vacuum of the cavity and mechanical modes. In particular, when the cavity is driven by a squeezed field along the required squeezing parameter, it enables modifying the region of Z_{2}-broken phase and significantly reducing the coupling strength to reach QPTs. Furthermore, by coupling atoms to the cavity mode, the hybrid system can undergo a QPT at a hybrid critical point, which is cooperatively determined by the optomechanical and light-atom systems. These results suggest that this optomechanical system complements other phase transition models for exploring novel critical phenomena.

Electron-Photon Chern Number in Cavity-Embedded 2D Moiré Materials

We explore theoretically how the topological properties of 2D materials can be manipulated by cavity quantum electromagnetic fields for both resonant and off-resonant electron-photon coupling, with a focus on van der Waals moiré superlattices. We investigate an electron-photon topological Chern number for the cavity-dressed energy minibands that is well defined for any degree of hybridization and entanglement of the electron and photon states. While an off-resonant cavity mode can renormalize electronic topological phases that exist without cavity coupling, we show that when the cavity mode is resonant to electronic miniband transitions, new and higher electron-photon Chern numbers can emerge.

Cavity Light-Matter Entanglement through Quantum Fluctuations

The hybridization between light and matter forms the basis to achieve cavity control over quantum materials. In this Letter we investigate a cavity coupled to a quantum chain of interacting spinless fermions by numerically exact solutions and perturbative analytical expansions. We draw two important conclusions about such systems: (i) Specific quantum fluctuations of the matter system play a pivotal role in achieving entanglement between light and matter; and (ii) in turn, light-matter entanglement is a key ingredient to modify electronic properties by the cavity. We hypothesize that quantum fluctuations of those matter operators to which the cavity modes couple are a general prerequisite for light-matter entanglement in the ground state. Implications of our findings for light-matter-entangled phases, cavity-modified phase transitions in correlated systems, and measurement of light-matter entanglement through Kubo response functions are discussed.

Non-Fermi-Liquid Behavior from Cavity Electromagnetic Vacuum Fluctuations at the Superradiant Transition

We study two-dimensional materials where electrons are coupled to the vacuum electromagnetic field of a cavity. We show that, at the onset of the superradiant phase transition towards a macroscopic photon occupation of the cavity, the critical electromagnetic fluctuations, consisting of photons strongly overdamped by their interaction with electrons, can in turn lead to the absence of electronic quasiparticles. Since transverse photons couple to the electronic current, the appearance of non-Fermi-Liquid behavior strongly depends on the lattice. In particular, we find that in a square lattice the phase space for electron-photon scattering is reduced in such a way to preserve the quasiparticles, while in a honeycomb lattice the latter are removed due to a nonanalytical frequency dependence of the damping ∝|ω|^{2/3}. Standard cavity probes could allow us to measure the characteristic frequency spectrum of the overdamped critical electromagnetic modes responsible for the non-Fermi-liquid behavior.

Perfect intrinsic squeezing at the superradiant phase transition critical point

Some of the most exotic properties of the quantum vacuum are predicted in ultrastrongly coupled photon-atom systems; one such property is quantum squeezing leading to suppressed quantum fluctuations of photons and atoms. This squeezing is unique because (1) it is realized in the ground state of the system and does not require external driving, and (2) the squeezing can be perfect in the sense that quantum fluctuations of certain observables are completely suppressed. Specifically, we investigate the ground state of the Dicke model, which describes atoms collectively coupled to a single photonic mode, and we found that the photon-atom fluctuation vanishes at the onset of the superradiant phase transition in the thermodynamic limit of an infinite number of atoms. Moreover, when a finite number of atoms is considered, the variance of the fluctuation around the critical point asymptotically converges to zero, as the number of atoms is increased. In contrast to the squeezed states of flying photons obtained using standard generation protocols with external driving, the squeezing obtained in the ground state of the ultrastrongly coupled photon-atom systems is resilient against unpredictable noise.

Coherent Plasma in a Lattice

We present a fully second-quantized calculation showing the emergence of spontaneous coherent configurations of the electromagnetic field interacting with charged bosons in a regular lattice. The bosons tend to oscillate at their plasma frequency, and in addition are subjected to electrostatic forces which keep them confined close to the lattice sites while causing a frequency shift in the oscillation. Under certain conditions upon these frequencies, we find that a suitably defined set of coherent states (coherent both in the field and matter degrees of freedom) exhibit a negative energy gap with respect to the perturbative ground state. This is true in the RWA approximation and for position-independent fields to both the first and second order in the interaction Hamiltonian. We compare this result with other recent findings from cavity QED, and note that (1) consideration of full 3D wavefunctions and a careful definition of the coherent states are essential for obtaining the energy gap, and (2) although our calculation is made in reference to bosons, it may apply to protons bound in a crystal matrix as well if their density is very low compared to the density of available states.

Photon Condensation and Enhanced Magnetism in Cavity QED

A system of magnetic molecules coupled to microwave cavities (LC resonators) undergoes the equilibrium superradiant phase transition. The transition is experimentally observable. The effect of the coupling is first illustrated by the vacuum-induced ferromagnetic order in a quantum Ising model and then by the modification of the magnetic phase diagram of Fe_{8} dipolar crystals, exemplifying the cooperation between intrinsic and photon-induced spin-spin interactions. Finally, a transmission experiment is shown to resolve the transition, measuring the quantum electrodynamical control of magnetism.

Manipulating matter by strong coupling to vacuum fields

Over the past decade, there has been a surge of interest in the ability of hybrid light-matter states to control the properties of matter and chemical reactivity. Such hybrid states can be generated by simply placing a material in the spatially confined electromagnetic field of an optical resonator, such as that provided by two parallel mirrors. This occurs even in the dark because it is electromagnetic fluctuations of the cavity (the vacuum field) that strongly couple with the material. Experimental and theoretical studies have shown that the mere presence of these hybrid states can enhance properties such as transport, magnetism, and superconductivity and modify (bio)chemical reactivity. This emerging field is highly multidisciplinary, and much of its potential has yet to be explored.