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arXiv:1008.0115 · Scientia Iranica

Cavity quantum electrodynamics in the ultrastrong coupling regime

E. Ahmadi, Hamidreza Chalabi, A. Arab, Sina Ataollah Khorasani

Published Jun 1, 2011• 9 citations
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Abstract

We revisit the mathematical formulation of the famous Jaynes–Cummings–Paul Hamiltonian, which describes the interaction of a two-level atom with a single mode of an electromagnetic cavity reservoir. We rigorously show that under the condition of ultrastrong coupling between the atom and cavity in which the transition frequency is comparable to the coupling frequency, the bosonic field operators undergo non-sinusoidal time variations. As a result, the well-known solutions to the Jaynes–Cummings–Paul model are no longer valid, even when the rotating wave approximation is not used. We show how a correct mathematical solution could be found instead.

DOI
10.1016/j.scient.2011.06.009

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We revisit the mathematical formulation of the famous Jaynes–Cummings–Paul Hamiltonian, which describes the interaction of a two-level atom with a single mode of an electromagnetic cavity reservoir. We rigorously show that under the condition of ultrastrong coupling between the atom and cavity in which the transition frequency is comparable to the coupling frequency, the bosonic field operators undergo non-sinusoidal time variations. As a result, the well-known solutions to the Jaynes–Cummings–Paul model are no longer valid, even when the rotating wave approximation is not used. We show how a correct mathematical solution could be found instead.
The interaction of quantum radiation and a two-level atom is described in the context through the Jaynes-Cummings-Paul Hamiltonian which is obtained through Heisenberg's interaction picture of the Atom-Radiation Hamiltonian. We argue that such a transformation is not mathematically exact in case of ultrastrong coupling, where the coupling rate is comparable to the transition frequency, and leads to erroneous results. In addition, we introduce an exact mathematical solution to calculate optical spectrum of this system.
We propose a reliable scheme to realize the ultrastrong Jaynes-Cummings (JC) model by simultaneously modulating the resonance frequencies of the two-level system and the bosonic mode in the ultrastrong quantum Rabi model. We find that in both the high- and low-frequency modulation regimes, the counter-rotating terms can be completely suppressed without reducing the coupling strength of the rotating-wave terms, and hence the ultrastrong JC Hamiltonian is achieved. The ultrastrong JC interaction can not only be used to implement ultrafast quantum operations such as ultrafast quantum state transfer and quantum logic gates but also will open up a new route to the demonstration of quantum phase transition associated with the JC Hamiltonian across the deep-strong-coupling point. Some discussions on the experimental implementation of this scheme with circuit-QED systems are presented.
We consider a two-level system such as a two-level atom, interacting with a cavity field mode in the rotating wave approximation, when the atomic transition frequency or the field mode frequency is periodically driven in time. We show that in both cases, for an appropriate choice of the modulation parameters, the state amplitudes in a generic nnn-excitation subspace obey the same equations of motion that can be obtained from a static non-Hermitian Jaynes-Cummings Hamiltonian with PT\mathcal{PT}PT symmetry, that is with an imaginary coupling constant. This gives further support to recent results showing the possible physical interest of PT\mathcal{PT}PT symmetric non-Hermitian Hamiltonians. We also generalize the well-known diagonalization of the Jaynes-Cummings Hamiltonian to the non-Hermitian case in terms of pseudobosons and pseudofermions, and discuss relevant mathematical and physical aspects.
Strong coupling between a single resonator mode and a single quantum emitter is key to a plethora of experiments and applications in quantum science and technology and is commonly described by means of the Jaynes–Cummings model. Here, we show that the Jaynes–Cummings model only applies when the cavity does not significantly change the emitter’s decay rate into free-space. Most notably, the predictions made by the Jaynes–Cummings model become increasingly wrong when approaching the ideal emitter-resonator systems with no free-space decay channels. We present a Hamiltonian that provides, within the validity range of the rotating wave approximation, a correct theoretical description that applies to all regimes. As minimizing the coupling to free-space modes is paramount for many cavity-based applications, a correct description of strong light-matter interaction is therefore crucial for developing and optimizing quantum protocols.
Strong coupling between a single resonator mode and a single quantum emitter is key to a plethora of experiments and applications in quantum science and technology and is commonly described by means of the Jaynes-Cummings model. Here, we show that the Jaynes-Cummings model only applies when the cavity does not significantly change the emitter's emission rate into free-space. Most notably, the predictions made by the Jaynes-Cummings model become increasingly wrong when approaching the ideal emitter-resonator systems with no free-space decay channels. We present a Hamiltonian that provides, within the validity range of the rotating wave approximation, a correct theoretical description that applies to all regimes. As minimizing the coupling to free-space modes is paramount for many cavity-based applications, a correct description of strong light-matter interaction is therefore crucial for developing and optimizing quantum protocols.
It is well known that, under the rotating-wave approximation, the Rabi Hamiltonian, which describes the interaction between a two-level atom and a single field mode, reduces to the Jaynes-Cummings model through exclusion of its counter-rotating term. In this work, it is found that, since photons in the mode are indistinguishable, there exist two conditions where the counter-rotating term can never be ignored. These conditions, all subject to the requirements that the atom-mode coupling is weak and the atom is initially in its ground state, are obtained in the stationary perturbation theory and confirmed through an analysis of the atom-mode system's evolution.