This paper connects the complementary limits of manipulating quantum many-body systems with classical light and quantum light. The authors describe two different pathways towards achieving Floquet engineering of matter: (i) many-photon states at weak light-matter coupling, or (ii) few-photon states at strong coupling.
The ultrastrong coupling regime has emerged as a fascinating and distinctive phenomenon in cavity-QED and light-matter interactions, where the occupation of virtual excitations (e.g., photons) is possible in vacuum, which is a consequence of counter-rotating wave effects and breaking U(1) symmetry. However, an ongoing challenge is how to convert these virtual photons into real photons. We will first discuss how to “Floquet engineer” the quantum Rabi model for a two-level system coupled to a quantized cavity mode, under periodic modulation of the cavity-dipole coupling rate, leading to rich Floquet states. Exploiting the quantum vacuum, in the ultrastrong coupling regime, we show how purely mechanical driving can produce real photons. These periodic driving schemes are promising for the coherent manipulation of hybrid quantum systems and quantum vacuum effects, with applications for quantum state engineering and the study of nonequilibrium quantum phenomena.
Light-matter strong coupling has been the subject of much attention in recent decades, giving optical systems unique features. However, properties of a system with strong coupling are determined by the properties of its components and are thus difficult to control. Here, we propose Floquet engineering, a technique of controlling the energy levels of a quantum system using external fields, as a method of manipulating a hybrid system of a molecule strongly coupled to a single-mode resonator. We show that an external field can change the relative positions of levels in an open strongly coupled system, leading to a change in the rates of transitions between them. We demonstrate that if the frequency of the pumping wave is close to polariton transitions in the hybrid system, nonmonotonic dependence of fluorescence and scattering amplitudes on pump intensity with a narrow resonance-like response occurs. We show that this phenomenon occurs due to hybridization of the lower and upper polaritons with substantially different excitation numbers caused by the pumping affecting polariton states of the system. This occurs when the Rabi interaction with the coherent field is comparable to the field-matter coupling constant, which in turn needs to be sufficient for the manifestation of strong coupling. This nonmonotonic dependence of the fluorescence and scattering amplitudes on pump rate intensity paves the way for the creation of nonlinear optical devices.
Subjecting a physical system to a time-periodic drive can substantially modify its properties and applications. This Floquet-engineering approach has been extensively applied to a wide range of classical and quantum settings in view of designing synthetic systems with exotic properties. Considering a general class of two-mode nonlinear optical devices, we show that effective optical nonlinearities can be created by subjecting the light field to a repeated pulse sequence, which couples the two modes in a fast and time-periodic manner. The strength of these drive-induced optical nonlinearities, which include an emerging four-wave mixing, can be varied by simply adjusting the pulse sequence. This leads to topological changes in the system's phase space, which can be detected through light intensity and phase measurements. Our proposal builds on an effective-Hamiltonian approach, which derives from a parent quantum many-body Hamiltonian describing driven interacting bosons. As a corollary, our results equally apply to Bose-Einstein condensates in driven double-well potentials, where pair tunneling effectively arises from the periodic pulse sequence. Our scheme offers a practical route to engineer and finely tune exotic nonlinearities and interactions in photonics and ultracold quantum gases.
Experimental progress in atomic, molecular and optical physics, at the quantum level, as well as in condensed matter physics, has over the last few decades allowed us to not only observe quantum phenomena in nature, but also control them. This has led to the idea of “engineering” quantum systems, where microscopic constituents, such as single atoms, are manipulated in a precise manner to achieve some desired behaviour. By now, this has become a central theme in contemporary low-energy quantum physics. The change in viewpoint, from “observing” to “controlling,” leads to very different goals and opportunities, for experimentalists and theorists alike. This thesis contains seven publications on the following two related topics: i) engineering interactions in quantum systems, allowing for a large degree of control of system parameters, and ii) quantifying and understanding quantum correlations in dynamical quantum systems. The latter is an important goal in quantum information science, necessary to take advantage of quantum systems for information processing tasks, and thus expected to be central for future quantum technologies
Light enables manipulating many-body states of matter, and atoms trapped in optical lattices is a prominent example. However, quantum properties of light are completely neglected in all quantum gas experiments. Extending methods of quantum optics to many-body physics will enable phenomena unobtainable in classical optical setups. We show how using the quantum optical feedback creates strong correlations in bosonic and fermionic systems. It balances two competing processes, originating from different fields: quantum backaction of weak optical measurement and many-body dynamics, resulting in stabilized density waves, antiferromagnetic and NOON states. Our approach is extendable to other systems promising for quantum technologies.
Floquet engineering and cavity quantum electrodynamics represent two complementary descriptions of light-matter interaction, yet their precise connection beyond the small-coupling regime remains subtle. Here, by representing the cavity field in a large-photon-number phase basis, we show that the time-dependent Schrödinger equation of a classically driven system emerges directly from the fully quantized problem, without replacing the field by a classical trajectory or assuming a mean-field decoupling. This establishes a one-to-one correspondence between quasienergies and photon-sector-shifted quantum energies, while providing a direct quantum interpretation of the Floquet mean energy and Anandan phase. Because gauge invariance is exactly preserved at the level of the quantum Hamiltonian, the quantum-to-classical correspondence remains valid beyond perturbative and small-coupling regimes. We further show that light--matter entanglement is encoded in matter--harmonic correlations of the corresponding Floquet mode, thus identifying a semiclassical limit in which Floquet physics emerges without requiring the quantum field itself to approach a coherent classical state.