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arXiv:1510.02118 · Physical Review A

Fock-space localization of polaritons in the Jaynes-Cummings dimer model

Hassan Shapourian, Darius J Sadri

Published Jan 22, 2016• 8 citations
arXivHTMLPDF

Abstract

We present a method to study the semiclassical dynamics of the Jaynes-Cummings dimer model, describing two coupled cavities, each containing a two-level system (qubit). We develop a Fock-space WKB approach in the polariton basis where each site is treated exactly while the intersite polariton hopping is treated semiclassically. We show that the self-trapped states can be viewed as Fock-space localized states. We find that this picture yields the correct critical value of interaction strength at which the delocalization-localization transition occurs. Moreover, the validity of our WKB approach is supported by showing that the quantum spectrum can be derived from a set of Bohr-Sommerfeld quantization conditions and by confirming that the quantum eigenstates are consistent with the classical orbital motion in the polariton band picture. The underlying idea of our method is quite general and can be applied to other interacting spin-boson models.

DOI
10.1103/physreva.93.013845

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We present a method to study the semiclassical dynamics of the Jaynes-Cummings dimer model, describing two coupled cavities, each containing a two-level system (qubit). We develop a Fock-space WKB approach in the polariton basis where each site is treated exactly while the intersite polariton hopping is treated semiclassically. We show that the self-trapped states can be viewed as Fock-space localized states. We find that this picture yields the correct critical value of interaction strength at which the delocalization-localization transition occurs. Moreover, the validity of our WKB approach is supported by showing that the quantum spectrum can be derived from a set of Bohr-Sommerfeld quantization conditions and by confirming that the quantum eigenstates are consistent with the classical orbital motion in the polariton band picture. The underlying idea of our method is quite general and can be applied to other interacting spin-boson models.
We consider the Jaynes-Cummings model of a single quantum spin sss coupled to a harmonic oscillator in a parameter regime where the underlying classical dynamics exhibits an unstable equilibrium point. This state of the model is relevant to the physics of cold atom systems, in non-equilibrium situations obtained by fast sweeping through a Feshbach resonance. We show that in this integrable system with two degrees of freedom, for any initial condition close to the unstable point, the classical dynamics is controlled by a singularity of the focus-focus type. In particular, it displays the expected monodromy, which forbids the existence of global action-angle coordinates. Explicit calculations of the joint spectrum of conserved quantities reveal the monodromy at the quantum level, as a dislocation in the lattice of eigenvalues. We perform a detailed semi-classical analysis of the associated eigenstates. Whereas most of the levels are well described by the usual Bohr-Sommerfeld quantization rules, properly adapted to polar coordinates, we show how these rules are modified in the vicinity of the critical level. The spectral decomposition of the classically unstable state is computed, and is found to be dominated by the critical WKB states. This provides a useful tool to analyze the quantum dynamics starting from this particular state, which exhibits an aperiodic sequence of solitonic pulses with a rather well defined characteristic frequency.
We study the coherence and fluorescence properties of the coherently pumped and dissipative Jaynes-Cummings-Hubbard model describing polaritons in a coupled-cavity array. At weak hopping we find strong signatures of photon blockade similar to single-cavity systems. At strong hopping the state of the photons in the array depends on its size. While the photon blockade persists in a dimer consisting of two coupled cavities, a coherent state forms on an extended lattice, which can be described in terms of a semiclassical model.
Abstract We have experimentally observed the dynamics of a single polariton and two polaritons in a two-ion chain. By driving two trapped ions at a motional blue-sideband (BSB) transition, we realize the anti-Jaynes–Cummings–Hubbard (JCH) model. When a single polariton exists in a trapped-ion chain, the polariton hops between the ion sites. On the other hand, when there are single polaritons at each ion site, the hopping of the polaritons is suppressed because of the polariton–polariton interaction induced by the nonlinearity of the anti-Jaynes–Cummings (JC) interaction, thereby realizing the blockade of polariton hopping in the anti-JCH model with trapped ions. Our work is a step towards the development of a trapped-ion based quantum simulator for strongly interacting polaritonic systems.
We investigate the nonequilibrium dynamics of a Josephson-coupled Jaynes-Cummings dimer in the presence of Kerr nonlinearity, which can be realized in the cavity and circuit quantum electrodynamics systems. The semiclassical dynamics is analyzed systematically to chart out a variety of photonic Josephson oscillations and their regime of stability. Different types of transitions between the dynamical states lead to the self-trapping phenomenon, which results in photon population imbalance between the two cavities. We also study the dynamics quantum mechanically to identify characteristic features of different steady states and to explore fascinating quantum effects, such as spin dephasing, phase fluctuation, and revival phenomena of the photon field, as well as the entanglement of spin qubits. For a particular "self-trapped" state, the mutual information between the atomic qubits exhibits a direct correlation with the photon population imbalance, which is promising for generating photon mediated entanglement between two non interacting qubits in a controlled manner. Under a sudden quench from stable to unstable regime, the photon distribution exhibits phase space mixing with a rapid loss of coherence, resembling a thermal state. Finally, we discuss the relevance of the new results in experiments, which can have applications in quantum information processing and quantum technologies.
A cavity quantum electrodynamics (cavity-QED) system combines two or more distinct quantum components, exhibiting features not seen in the individual systems. In this work, we study the one-dimensional Jaynes-Cummings-Hubbard model in the two-excitation (two-polariton) subspace. We find that the centre momentum of two-excitation induces a magnetic flux piercing the equivalent Hamiltonian Hk in the invariant subspace with momentum k, which can be described as a 4-leg ladder in the auxiliary space. Furthermore, it is shown that the system in π-centre-momentum subspace is equivalent to a lattice system for spin-1 particle with spin-orbit coupling. On the basis of this concise description, a series of bound-pair eigenstates which display long-range polaritonic entanglement is presented as a simple application.
The nature of the ground states for a system composed of two coupled cavities with each containing a pair of dipole-coupled two-level atoms are studied over a wide range of detunings and dipole coupling strengths. The cases for three limits of exact resonance, large positive and negative detunings are discussed, and four types of the ground states are revealed. Then the phase diagrams of the ground state are plotted by choosing three different "order parameters". We find that the phase space, determined by the combinative action of detuning and the dipole coupling strength, is divided into four regions. This is different from the general Bose-Hubbard model and more richer physics are presented in the two-site coupled cavities system. That is, the insulator region may be polaritonic or atomic and the superfluid region may be polaritonic or photonic in nature.