We consider the dynamical behavior of light in a cavity that contains birefringent elements with time-dependent settings. The evolution of the two-dimensional polarization vector can be described by an equation of the Schr\"odinger type if the intracavity elements change little on the time scale of the round-trip time. A coupled-mode analysis is given, which models the multimode dynamics of the optical system. We show that a description in terms of isolated two-level systems is justified if the optical band gap is small.
We consider the dynamical behavior of light in a cavity that contains birefringent elements with time-dependent settings. The evolution of the two-dimensional polarization vector can be described by an equation of the Schr"odinger type if the intracavity elements change little on the time scale of the round-trip time. A coupled-mode analysis is given, which models the multimode dynamics of the optical system. We show that a description in terms of isolated two-level systems is justified if the optical band gap is small.
We present the effects of resonator birefringence on the cavity-enhanced interfacing of quantum states of light and matter, including the first observation of single photons with a time-dependent polarization state that evolves within their coherence time. A theoretical model is introduced and experimentally verified by the modified polarization of temporally long single photons emitted from a ^{87}Rb atom coupled to a high-finesse optical cavity by a vacuum-stimulated Raman adiabatic passage process. Further theoretical investigation shows how a change in cavity birefringence can both impact the atom-cavity coupling and engender starkly different polarization behavior in the emitted photons. With polarization a key resource for encoding quantum states of light and modern micron-scale cavities particularly prone to birefringence, the consideration of these effects is vital to the faithful realization of efficient and coherent emitter-photon interfaces for distributed quantum networking and communications.
Summary form only given. We perform a theoretical and numerical analysis of a system comprising a Bose-Einstein condensate (BEC) interacting with a laser beam in an optical cavity. Recent studies have modelled this system with two motional modes coupled with a light mode and have shown nonlinear behaviour, e.g. bistability [1,2]. Our approach tackles the full Gross-Pitaevskii equation coupled to the cavity field as well as expansions in a number of motional modes.We consider a fixed value of the cavity-pump detuning and increase the pump intensity to cross the region of bistability (see Fig. 1 left panel). The system then displays a variety of behaviours, including regular oscillations, chaotic dynamics, and quasi-periodic behaviour, as displayed in the right panel of Fig. 1. In Fig. 1 we have used a coupled-equation system comprising the Schrödinger wave equation and a cavity-field evolution [3], where we have adiabatically eliminated the latter leading to a conservative dynamics. The chaotic dynamics here is not induced by the detector noise and is an intrinsic property of the light-BEC interaction.Our second model considers a multiple-modes expansion. By using just three modes, the chaotic dynamics observed in the full simulation is recovered. The bifurcation structure, typical of conservative dynamics in the vicinity of a separatrix, is identified through the use of projections and power spectra. Our results suggest that chaotic oscillations in this system are deterministic in nature and arise purely from nonlinear effects. In more general terms, the model is a novel example of quantum matter exhibiting chaotic behaviour and invites further research.
We compare theoretical predictions and experimental data for the multimode instability of optical bistability, which arises from the coherent dynamics of a system of two-level molecules contained in an optical cavity and driven by an external stationary laser field. Considerable insight into this phenomenon is provided by two ``rules of thumb'' that govern the behavior of the self-pulsing frequency, and establish its relation with the Rabi frequency of the intracavity field. We describe in detail the experimental apparatus and the main features of the experimental findings. The theoretical results are based on the Maxwell-Bloch equations for a ring cavity in the plane-wave approximation. Despite the crudeness of this model, the numerical data display a satisfactory qualitative agreement with the experimental results. Additional period-doubling and chaotic phenomena, predicted by the theory and not observed in the experiment, are presumably washed out by the longitudinal and radial variation of the electric field in the cavity.
We present a full quantum theory for the dissipative dynamics of an optical cavity in the ultrastrong light-matter coupling regime, in which the vacuum Rabi frequency is a significant fraction of the active electronic transition frequency and the antiresonant terms of the light-matter coupling play an important role. In particular, our model can be applied to the case of intersubband transitions in doped semiconductor quantum wells embedded in a microcavity. The coupling of the intracavity photonic mode and of the electronic polarization to the external, frequency-dependent, dissipation baths is taken into account by means of quantum Langevin equations in the input-output formalism. In the case of a time-independent vacuum Rabi frequency, exact analytical expressions for the operators are obtained, which allows us to characterize the quantum dissipative response of the cavity to an arbitrary initial condition (vacuum, coherent field, thermal excitation). For a vacuum input in both the photonic and electronic polarization modes, the ground state of the cavity system is a two-mode squeezed vacuum state with a finite population in both photonic and electronic modes. These excitations are, however, virtual and cannot escape from the cavity: for a vacuum input, a vacuum output is found, without any trace of the intracavity squeezing. For a coherent photonic input the linear optical response spectra (reflectivity, absorption, transmission) have been studied, and signatures of the ultrastrong coupling have been identified in the asymmetric and peculiar anticrossing of the polaritonic eigenmodes. Finally, we have calculated the electroluminescence spectra in the case of an incoherent electronic input: the emission intensity in the ultrastrong coupling regime results in being significantly enhanced as compared to the case of an isolated quantum well without a surrounding cavity.
We report on the experimental realization and theoretical analysis of four-level systems produced in passive optical ring cavities by introducing various intracavity elements. Birefringent elements couple waves with different polarizations and thus lift the polarization degeneracy of the cavity modes. Reflecting elements couple waves propagating in different directions and lift the propagation degeneracy. A combination of these elements leads, in general, to a splitting of every longitudinal cavity mode into a four-mode system. Under the restriction that the optical components are loss-free, the description of these ring cavities in a transmission-matrix formalism leads in a natural way to the study of the Lie group U(2,2) and its Lie algebra u(2,2). We associate each of the 16 generators of this algebra with a specific type of optical element, some of which are standard components, others not. From the commutation relations of the generators, we derive a recipe for the construction of the nonstandard components as a sequence of standard ones. It follows that the entire U(2,2) group can actually be realized. The number of independent parameters---16 for a general U(2,2) element---is shown to be reduced substantially if the optical components are selected out of a restricted number of types, provided that the corresponding generators define a subalgebra of u(2,2). In such cases, a subgroup of U(2,2) is realized and the number of independent parameters of the optical system is given by the number of generators of the subalgebra. A connection is established between the subalgebras and symmetry properties of the optical components in the cavity. We consider the influence of symmetries on the mode structure and consider our experimental results from this viewpoint. In particular, we discuss time-reversal invariance, leading to the symplectic group USp(2,2), and we identify antiunitary symmetries leading to Kramers's degeneracy in the mode spectrum. We propose the application of the group U(2,2) in optics as a tool yielding direct practical results.
The enhanced interaction of quantum states of light and matter within an optical resonator is a powerful tool for both addressing fundamental questions of nature and pursuing quantum technologies. Here, we discuss the impact of cavity birefringence - a lifting of the degeneracy of polarisation modes within the resonator - on both of these challenges. A novel model for such systems is experimentally verified by the cavity emission of single photons with time-dependent polarisation states that evolve along their wavepacket [1]. This model is then used to demonstrate how a tailored birefringence allows for enhanced photon emission beyond previous limitations [2].