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Physical Review A

Single-photon state in a driven Jaynes-Cummings system

Hyunchul Nha, Young-Tak Chough, Kyungwon An

Published Nov 30, 2000• 18 citations
Publisher

Abstract

We present a practical scheme of preparing a temporally stationary single-photon-trapped state. A special dynamics at two-photon resonance in the coupled atom-cavity system, where a two-level atom is driven by a classical field, is investigated for this purpose. It is found that significant atomic damping is required, rather than avoided, to establish the one-photon Fock state. We analytically derive the optimal conditions in the large detuning limit.

DOI
10.1103/physreva.63.010301

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We present a practical scheme of preparing a temporally stationary single-photon-trapped state. A special dynamics at two-photon resonance in the coupled atom-cavity system, where a two-level atom is driven by a classical field, is investigated for this purpose. It is found that significant atomic damping is required, rather than avoided, to establish the one-photon Fock state. We analytically derive the optimal conditions in the large detuning limit.
We propose a scheme to realize a two-photon Jaynes-Cummings model for a single atom inside an optical cavity. It is shown that the interplay of a laser detuning and atom (cavity) pump (driven) field gives rise to the strong single photon blockade, two-photon bundles, and photon-induced tunneling. With the cavity driven field, strong photon blockade occurs in the weak coupling regime, and switching between single photon blockade and photon-induced tunneling at two-photon resonance are achievable via increasing the driven strength. By turning on the atom pump field, quantum switching between two-photon bundles and photon-induced tunneling at four-photon resonance are realized. More interestingly, the high-quality quantum switching between single photon blockade, two-photon bundles, and photon-induced tunneling at three-photon resonance is achieved with combining the atom pump and cavity driven fields simultaneously. In contrast to the standard two-level Jaynes-Cummings model, our scheme with generating a two-photon (multi-photon) Jaynes-Cummings model reveals a prominent strategy to engineer a series of special nonclassical quantum states, which may pave the way for investigating basic quantum devices to implement in quantum information processing and quantum networks.
In this paper, we generalize the ordinary two-photon Jaynes-Cummings model (TPJCM) by considering the atom (or ion) to be trapped in a simple harmonic well. A typical setup would be an optical cavity containing a single ion in a Paul trap. Due to the inclusion of atomic vibrational motion, the atom-field coupling becomes highly nonlinear what brings out quite different behaviors for the system dynamics when compared to the ordinary TPJCM. In particular, we derive an effective two-photon Hamiltonian with dependence on the number operator of the ion's center-of-mass motion. This dependence occurs both in the cavity induced Stark-shifs and in the ion-field coupling, and its role in the dynamics is illustrated by showing the time evolution of the probability of occupation of the electronic levels for simple initial preparations of the state of the system.
We propose a reliable scheme to recover the conventional photon blockade effect in the dispersive Jaynes-Cummings model, which describes a two-level atom coupled to a single-mode cavity field in the large-detuning regime. This is achieved by introducing a transversal driving to the atom and then photonic nonlinearity is obtained. The eigenenergy spectrum of the system is derived analytically and the photon blockade effect is confirmed by numerically calculating the photon-number distributions and equal-time second-order correlation function of the cavity field in the presence of system dissipations. We find that the conventional photon blockade effect can be recovered at proper atomic and cavity-field drivings. This work will provide a method to generate the conventional photon blockade effect in the dispersively coupled quantum optical systems.
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 dynamics of the much studied Jaynes–Cummings model, of a single two-level atom interacting with a single quantized field mode, is simple to solve for because the number of quanta in the system is strictly conserved. Including the effects of cavity damping makes the model significantly more difficult to treat. Here we present a simple derivation of the evolution of the atomic inversion in the presence of cavity damping. This will enable us to explain the physical meaning of the solution, first derived more than 20 years ago, and also to show that it is valid for much stronger damping than was appreciated at that time.