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arXiv:1905.13495 · Physical Review Letters

Chiral Light-Matter Interaction beyond the Rotating-Wave Approximation

Sahand Mahmoodian

Published Sep 26, 2019• 18 citations
arXivHTMLPDF

Abstract

I introduce and analyze chiral light-matter interaction in the ultrastrong coupling limit where the rotating-wave approximation cannot be made. Within this limit, a two-level system with a circularly polarized transition dipole interacts with a copolarized mode through rotating-wave terms. However, the counterrotating terms allow the two-level system to couple to a counterpolarized mode with the same coupling strength, i.e., one that is completely decoupled within the rotating-wave approximation. Although such a Hamiltonian is not particle number conserving, the conservation of angular momentum generates a U(1) symmetry which allows constructing an ansatz. The eigenstates and dynamics of this novel model are computed for single-cavity interactions and for a many-mode system. The form of the ansatz provides significant analytic insight into the physics of the ground state and the dynamics; e.g., it indicates that the ground states are two-mode squeezed. This work has significant implications for engineering light-matter interaction and novel quantum many-body dynamics beyond the rotating-wave approximation.

DOI
10.1103/physrevlett.123.133603

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I introduce and analyze chiral light-matter interaction in the ultrastrong coupling limit where the rotating-wave approximation cannot be made. Within this limit, a two-level system with a circularly polarized transition dipole interacts with a copolarized mode through rotating-wave terms. However, the counterrotating terms allow the two-level system to couple to a counterpolarized mode with the same coupling strength, i.e., one that is completely decoupled within the rotating-wave approximation. Although such a Hamiltonian is not particle number conserving, the conservation of angular momentum generates a U(1) symmetry which allows constructing an ansatz. The eigenstates and dynamics of this novel model are computed for single-cavity interactions and for a many-mode system. The form of the ansatz provides significant analytic insight into the physics of the ground state and the dynamics; e.g., it indicates that the ground states are two-mode squeezed. This work has significant implications for engineering light-matter interaction and novel quantum many-body dynamics beyond the rotating-wave approximation.
The interaction of confined atoms with a single mode radiation field is the main subject in the theory of cavity quantum electrodynamics . The constraints imposed by the cavity on matter and radiation fields give rise to collective phenomena. One possible outcome is the enhanced and coherent spontaneous emission of photons by the atoms: the superradiance. As predicted by Dicke, conservation laws are essential in superradiance and are derived from the matter-interaction Hamiltonian . Here, we consider N two-level ultracold atoms interacting with a single mode bosonic field, in the Dicke Hamiltonian, and trapped inside a non-dissipative optical cavity . Numerical and analytical results derived from finite size regime indicate the matter–radiation coupling strength, λ , is insufficient to draw the complete picture of the system. Instead, they support the relevance of U ( 1 ) symmetry, which prompts the study of (i) particle and angular momentum conservation, (ii) the constraints imposed to correlation functions and (iii) the influence of symmetries in the system dynamics . Further exploring the U ( 1 ) and rotational symmetries permits a simple interpretation of antirotating contributions as spin–orbit operators. As application, we show two species of ultracold clouds develop interactions due to antirotating operators.
The interplay of three light-matter interaction processes, i.e., rotating and counterrotating interactions and two-photon relaxation of the light field, is a topic of interest in quantum optics and quantum information processing. In this work we investigate theoretically the three light-matter interaction processes using the anisotropic Rabi model, which accounts for different strengths of rotating and counterrotating interactions and the unique occurrence of photon escape exclusively in pairs. By numerically solving the Lindblad master equation, we analyze the excitation-relaxation dynamics and derive a non-Hermitian effective Hamiltonian to gain further physical insights. To explore the individual effects of these interactions, we examine three analytically tractable limits of the effective Hamiltonian. Our analysis reveals that the three competitive light-matter interaction processes exhibit sensitivity to parity, leading to intriguing phenomena in both transient and steady states. Particularly interesting dynamical patterns resembling quantum phase transitions emerge when these three interaction terms compete. This work deepens the understanding of ultrastrong light-matter interaction in open quantum systems and offers valuable insights into cavity-based quantum computations.
The Dicke model (DM) serves as a paradigm for understanding collective light-matter interactions. We introduce the chiral Dicke model, a generalization where an atomic ensemble couples to a two-mode cavity via chiral interactions. Unlike the standard DM, the chiral DM is endowed with an inherent continuous U(1)U(1)U(1) symmetry associated with angular momentum conservation. The ground-state phase diagram and the associated quantum phase transitions are charted out, revealing a U(1)U(1)U(1)-broken superradiant phase that spans a broad parameter space. We demonstrate that the spectrum of quantum fluctuations is highly tunable in both the symmetric and broken phases. Strikingly, our calculations reveal that the system exhibits `multiversality', where distinct universality classes govern the transition between the same two phases. In particular, along a special line in parameter space, the dynamical critical exponent for the normal-superradiant phase transition changes from zν=1zν=1zν=1 to zν=1/2zν=1/2zν=1/2. Our work establishes the chiral Dicke model as a powerful platform to realize novel quantum phases and multiversal critical phenomena in light-matter coupled systems.
The Tavis-Cummings model for more than one qubit interacting with a common oscillator mode is extended beyond the rotating wave approximation (RWA). We explore the parameter regime in which the frequencies of the qubits are much smaller than the oscillator frequency and the coupling strength is allowed to be ultrastrong. The application of the adiabatic approximation introduced by Irish et al. [Phys. Rev. B 72, 195410 (2005)] for a single-qubit system is extended to the multiqubit case. For a two-qubit system, we identify three-state manifolds of close-lying dressed energy levels and obtain results for the dynamics of intramanifold transitions that are incompatible with results from the familiar regime of the RWA. We exhibit features of two-qubit dynamics that are different from the single-qubit case, including calculations of qubit-qubit entanglement. Both number state and coherent state preparations are considered, and we derive analytical formulas that simplify the interpretation of numerical calculations. Expressions for individual collapse and revival signals of both population and entanglement are derived.
The rotating-wave approximation (discarded of counter-rotating interactions) to light-matter interactions is widely used in the quantum electrodynamics Hamiltonian; however, its validity has long been a matter of debate. In this article, we explore the importance of counter-rotating interactions in the quantum dynamics of multiple molecules in complex dielectric environments within the framework of macroscopic quantum electrodynamics. Through our analytical analysis, we find that, in the weak coupling regime, the lack of counter-rotating interactions results in the absence of the Casimir-Polder potentials (medium-assisted energy shifts) in the ground-state molecules and a significant deviation of the intermolecule dipole-dipole interactions. Notably, the deviation of intermolecule dipole-dipole interaction can reach up to 50 percent in the near-field zone (short intermolecule distance). We also conduct a case study on the population dynamics of a pair of identical molecules above a plasmonic surface. Through analytical and numerical analysis, it is revealed that the lack of counter-rotating interactions can profoundly affect the dynamics, especially the oscillatory pattern due to intermolecule dipole-dipole interactions, of the molecules in both strong and weak coupling regimes, emphasizing the need for careful consideration when making the rotating-wave approximation in a multiple-molecule system coupled with quantum light.
High Resolution Image Download MS PowerPoint Slide Spin-dependent, directional light–matter interactions form the basis of chiral quantum networks. In the solid state, quantum emitters commonly possess circularly polarized optical transitions with spin-dependent handedness. We demonstrate numerically that spin-dependent chiral coupling can be realized by embedding such an emitter in a waveguide-coupled nanocavity, which supports two near-degenerate, orthogonally polarized cavity modes. The chiral behavior arises due to direction-dependent interference between the cavity modes upon coupling to two single-mode output waveguides. Notably, an experimentally realistic cavity design simultaneously supports near-unity chiral contrast, efficient (>95%) cavity-waveguide coupling and enhanced light–matter interaction strength (Purcell factor F P > 70). In combination, these parameters enable the development of highly coherent spin–photon interfaces ready for integration into nanophotonic circuits.