The authors calculate the asymptotic quantum state of a driven cavity mode interacting with a two-state atom when the dipole coupling constant is much larger than the atomic and cavity linewidths. They show that a novel symmetry breaking transition occurs as the strength of the driving field is increased. Although the driving field, the cavity mode, and the atom are all resonant, above the transition threshold the intracavity field shows a bimodality in phase. The bimodality results from an intensity-dependent detuning between the driving field and the transition frequencies of the composite atom-cavity-mode 'molecule.' Well above the transition threshold the driven cavity mode plus atom behaves as a driven harmonic oscillator with randomly switched detuning; the detuning (and hence the phase of the interactivity field) changes sign each time the atom makes a spontaneous transition between dressed states.
The authors calculate the asymptotic quantum state of a driven cavity mode interacting with a two-state atom when the dipole coupling constant is much larger than the atomic and cavity linewidths. They show that a novel symmetry breaking transition occurs as the strength of the driving field is increased. Although the driving field, the cavity mode, and the atom are all resonant, above the transition threshold the intracavity field shows a bimodality in phase. The bimodality results from an intensity-dependent detuning between the driving field and the transition frequencies of the composite atom-cavity-mode 'molecule.' Well above the transition threshold the driven cavity mode plus atom behaves as a driven harmonic oscillator with randomly switched detuning; the detuning (and hence the phase of the interactivity field) changes sign each time the atom makes a spontaneous transition between dressed states.
The interaction between two-state atoms and the modes of an optical cavity has been studied extensively over many years; in particular, in connection with lasers and optical bistability. These are dissipative systems, and it has been usual in their study to assume that dissipation rates are, in some sense, large compared with the coupling strength between the atoms and the field. Recent work has shown that interesting new dynamical behavior occurs when this is not so. For example, spontaneous emission linewidths can be altered,1,2 and if the coupling is very strong, an emission line can be split into a pair of resonances identified with the normal- mode frequencies of coupled oscillators describing the atomic polarization and the cavity field.3.4 Altered linewidths and normal-mode splitting are features of weak excitation; both are explained by a coupled damped harmonic oscillator model. In this paper we report new results obtained for strong excitation.
We investigate the degree of entanglement between an atom and a driven cavity mode in the presence of dissipation. Previous work has shown that in the limit of weak driving fields, the steady-state entanglement is proportional to the square of the driving intensity. This quadratic dependence is due to the generation of entanglement by the creation of pairs of photons or excitations. In this work we investigate the entanglement between an atom and a cavity in the presence of multiple photons. Nonlinearity of the atomic response is needed to generate entanglement, but as that nonlinearity saturates the entanglement vanishes. We posit that this is due to spontaneous emission, which puts the atom in the ground state and the atom-field state into a direct product state. An intermediate value of the driving field, near the field that saturates the atomic response, optimizes the atom-field entanglement. In a parameter regime for which multiphoton resonances occur, we find that entanglement recurs at those resonances. In this regime, we find that the entanglement decreases with increasing photon number. We also investigate, in the bimodal regime, the entanglement as a function of atom and/or cavity detuning. Here we find that there is evidence of a phase transition in the entanglement, which occurs at $2\ensuremath{\epsilon}/g\ensuremath{\ge}1$.
The eigenstates of the Jaynes-Cummings Hamiltonian (the dressed atomic states) are widely used to describe the interaction between a single two-level atom and a single mode of the electromagnetic field. They provide a particularly useful basis when the secular approximation is justified. For an atom interacting fog with n photons in a cavity, the secular approximation requires that the n-photon Rabi frequency 2 n g be much larger than the atomic and cavity linewidths. Normally this condition is met when n is large and the coupling constant g is much smaller than the atomic and cavity linewidths. In this paper we allow g to be larger than the linewidths, and we allow the photon number to be small. We show that when the cavity is driven by a coherent field, the usual secular approximation cannot be used. The natural basis states become are now the eigenstates of the Jaynes-Cummings Hamiltonian plus the external field interaction. We solve this eigenvalue problem by separating the field and atomic parts of the Hamiltonian using a displacement and squeeze in the Hilbert-space of the field. We find that the Rabi frequencies are renormalized downwards as the strength of the driving field is increased. They eventually vanish at a critical field strength. At this critical field strength we observe a spontaneous symmetry breaking in the steady-state solution of the master equation for a single atom interacting with a driven cavity mode.
The coherent evolution of the atom–cavity state in bimodal (cavity) experiments has been analysed for a realistic time dependence in detuning the atomic transition frequency. Apart from a 'smooth switch' of the atomic resonance from one to the second mode of a bimodal cavity, we considered also an additional (effective) interaction between the field modes of the cavity, known as a 'communication channel'. Comparison of our model computations has been made especially with the measurements by Rauschenbeutel et al (2001 Phys. Rev. A 64 050301) who demonstrated for the first time the entanglement of the field modes in a bimodal cavity. It is shown that the agreement between the (theoretically) predicted and experimental phase shifts can be improved by allowing a 'communication' between the two field modes during a short but finite switch of the atomic transition frequency from one mode to the other. We therefore suggest that the details of the atom–cavity detuning should be taken into account for the future interpretation of bimodal cavity experiments.
A cavity-modified master equation is derived for a coherently driven two-level atom coupled to a single-mode cavity in the bad cavity limit, in which the cavity frequency is tuned to either the center or one of the sidebands of the Mollow triplet. The atomic populations in both the bare- and dressed-state representations are analyzed in terms of the cavity-modified transition rates. In the bare-state basis, the role of the cavity may be interpreted as enhancing the stimulated absorption of the atom while suppressing the stimulated emission. The bare-state population may thus be inverted under appropriate conditions. The dressed-state inversion, however, originates from the enhancement of the atom-cavity interaction when the cavity is resonant with the atomic dressed-state transition. We show that two-phase quadratures of the atomic polarization decay at different rates. The decay of the in-phase (or out-of-phase) quadrature may be greatly inhibited as the driving intensity increases, depending on the cavity resonant frequency. The spectrum of the atomic fluorescence emitted out the side of the cavity is also studied. The spectral profiles are sensitive to the cavity frequency. When the cavity frequency is tuned to the center of the Mollow resonances, the fluorescence spectrum is symmetrical with three peaks whose linewidths and heights are intensity dependent. When the cavity frequency is tuned to one of the Mollow sidebands, however, it is asymmetric, and the central peak and the sideband on resonance with the cavity can be significantly suppressed for strong driving fields. All three spectral lines can be narrowed by increasing the Rabi frequency. The physics of these striking spectral features is explored in the dressed-state basis. We also investigate the probe absorption spectrum. When the cavity frequency is tuned to the center of the Mollow fluorescence triplet, the central component exhibits a Lorentzian line shape, while the side bands show the Rayleigh-wing line shape. Probe gain may occur at line center due to cavity-induced, bare-state population inversion. When the cavity is tuned to resonance with one sideband, only two sidebands, with Lorentzian profiles, dominate. Gain can occur at the sideband far off resonant with the cavity. The sideband gain is a consequence of an unbalanced dressed-state population distribution.
We follow the passage from complex amplitude bistability to phase bistability in the driven dissipative Jaynes-Cummings oscillator. Quasi -distribution functions in the steady state are employed, for varying qubit-cavity detuning and drive parameters, in order to track a first-order dissipative quantum phase transition up to the critical point marking a second-order transition and spontaneous symmetry breaking. We demonstrate the photon blockade breakdown in the dispersive regime, and find that the coexistence of cavity states in the regime of quantum bistability is accompanied by pronounced qubit-cavity entanglement. Focusing on the effect of quantum-activated switching for both coupled degrees of freedom, we move from a region of minimal entanglement in the dispersive regime, where we derive analytical perturbative results, to the threshold behaviour of spontaneous dressed-state polarization at resonance.