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arXiv:2406.18822 · Physical Review A

Insensitivity of the two-photon Jaynes-Cummings model to thermal noise

Hiroo Azuma

Published Dec 17, 2024• 4 citations
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Abstract

We study the thermal effects of the multiphoton Jaynes-Cummings model (JCM) using a thermofield dynamics (TFD) method. Letting the initial state of the whole system for the multiphoton JCM be a product of the ground state of an atom and a coherent state of a cavity field at finite temperature, we compute its time evolution. We evaluate a period of the collapse and revival of the Rabi oscillations and the relative entropy of coherence of the atom up to the second-order perturbation of the low-temperature expansion. We show that an intuitive estimation of the period matches the result of the perturbation theory of TFD well. In particular, we see that the period of the two-photon JCM hardly depends on the amplitude of the coherent state of the cavity field or the temperature. Numerical calculations suggest that the relative entropy of coherence of the two-photon JCM does not decay even for nonzero-temperature cases as time proceeds. By contrast, the relative entropies of coherence for single-, three-, and four-photon JCMs decay as time proceeds for zero- and finite-temperature cases.

DOI
10.1103/physreva.110.063714

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We study the thermal effects of the multiphoton Jaynes-Cummings model (JCM) using a thermofield dynamics (TFD) method. Letting the initial state of the whole system for the multiphoton JCM be a product of the ground state of an atom and a coherent state of a cavity field at finite temperature, we compute its time evolution. We evaluate a period of the collapse and revival of the Rabi oscillations and the relative entropy of coherence of the atom up to the second-order perturbation of the low-temperature expansion. We show that an intuitive estimation of the period matches the result of the perturbation theory of TFD well. In particular, we see that the period of the two-photon JCM hardly depends on the amplitude of the coherent state of the cavity field or the temperature. Numerical calculations suggest that the relative entropy of coherence of the two-photon JCM does not decay even for nonzero-temperature cases as time proceeds. By contrast, the relative entropies of coherence for single-, three-, and four-photon JCMs decay as time proceeds for zero- and finite-temperature cases.
In this paper, we investigate thermal effects of the Jaynes–Cummings model (JCM) at finite temperature with a perturbative approach. We assume a single two-level atom and a single cavity mode to be initially in the thermal equilibrium state and the thermal coherent state, respectively, at a certain finite low temperature. Describing this system with Thermo Field Dynamics formalism, we obtain a low-temperature expansion of the atomic population inversion in a systematic manner. Letting the system evolve in time with the JCM Hamiltonian, we examine thermal effects of the collapse and the revival of the Rabi oscillations by means of the third-order perturbation theory under the low-temperature limit, that is to say, using the low-temperature expansion up to the third-order terms. From an intuitive discussion, we can expect that the period of the revival of the Rabi oscillations becomes longer as the temperature rises. Numerical results obtained with the perturbation theory reproduce well this temperature dependence of the period.
A two-level system driven by a classical single frequency field in rotating-wave approximation is a basic model for resonance in quantum optics. The probability of making a transition depends sinusoidally on time with a characteristic frequency called the Rabi frequency. The Jaynes-Cummings model (JCM) consists of a two-level atomic system driven by a single quantized electromagnetic field mode. The field entropy in the case of an atom interacting with an initially coherent field is expected to reflect the collapse and revival of Rabi oscillations. The photon statistics of the JCM are examined and the entropy concepts are used to describe the apparently disordered collapses. A density matrix method is used to describe the influence of photon statistics in the JCM. The quantum generalization defines entropy through where the trace is taken over a convenient basis set. The thermal field JCM shows enhanced photon variances as expected for an initially Bose-Einstein field with large fluctuations.
An alternative approach to the Jaynes–Cummings model (JCM) with dissipation at a finite environmental temperature is presented in terms of a new master equation under Born–Markovian approximation. An analytic solution of the dissipation JCM is obtained. A variety of physical quantities of interest are calculated analytically. Dynamical properties of the atom and the field are investigated in some detail. It is shown that both cavity damping and environmental temperature strongly affect nonclassical effects in JCM, such as collapse and revivals of the atomic inversion, oscillations of the photon-number distribution, quadrature squeezing of the field and sub-Poissonian photon statistics.
An alternative approach to the Jaynes-Cummings model (JCM) with dissipation at a finite enviromental temperature is presented in terms of a new master equation under Born-Markovian approximations. An analytic solution of the dissipation JCM is obtained. A variety of physical quantities of interest are calculated analytically. Dynamical properties of the atom and the field are investigated in some detail. It is shown that both cavity damping and environmental temperature strongly affect nonclassical effects in the JCM, such as collapse and revivals of the atomic inversion, oscillations of the photon-number distribution, quadrature squeezing of the field and sub-Poissonian photon statistics.
The dynamics of the Jaynes–Cummings (JCM) model with a nonlinear Kerr medium at initially thermal and squeezed vacuum fields is discussed. At a special choice of the detuning the Rabi frequency can have a minimum at the initial mean photon number [nbar]. Then the situation becomes especially interesting and instead of the first-order ‘usual’ revivals resembling those manifested by the standard coherent JCM, the nonlinear JCM exhibits second-order revivals, also for initially thermal and squeezed vacuum fields, at least for not too large [nbar]. The revival times are highly sensitive to the nature of [nbar]. In the first case the revival period of the oscillations is dependent on whether [nbar] is integer or non-integer (situation similar to an initially coherent field) while in the latter case it depends additionally on the parity of the integer [nbar]. Moreover, for the squeezed vacuum model appearance of the revivals at an integer [nbar] is accelerated when compared to coherent and thermal models.
Summary form only given. We study the behavior of classical and quantum correlations between a two level atom and a quantised electromagnetic field mode in a thermal state interacting according to the Jaynes Cummings model (JCM). This model predicts collapses and revivals of Rabi oscillations which is also seen in experiments, providing direct evidence for the quantum mechanical nature of the electromagnetic field. It also has an analytical solution for arbitrary coupling constants and can easily be extended to include a variety of initial conditions,dissipation and damping, multiple atoms, multilevel atoms, multimode fields and more elaborated interactions such as multiphoton or intensity-dependent interaction.