Multiphoton Jaynes-Cummings Model: Arbitrary Rotations in Fock Space and Quantum Filters

Abstract

The multiphoton Jaynes-Cummings model is investigated and applications in quantum information science are explored. Considering the strong atom-field coupling regime and an N -photon interaction, a nonlinear driving field can perform an arbitrary rotation in the Fock space of a bosonic mode involving the vacuum and an M -Fock state, with M < N . In addition, driving a bosonic mode with a linear coherent field (superposition of many Fock states), only the cavity states within the Fock subspace {|0 , |1 , . . . , |N − 1 } can be populated; i.e., we show how to implement a Fock state filter, or quantum scissor, that restricts the dynamics of a given bosonic mode to a limited Hilbert space. Such a device can be employed as a generator of finite-dimensional quantum-optical states and also as a quantum-optical intensity limiter, allowing as a special case the generation of single-photon pulses. On the other hand, our system also provides a very rich physics in the weak atom-field coupling regime, in particular multiphoton electromagnetically induced transparencylike phenomena, inducing a narrow (controllable) reflectivity window for nonlinear probe fields. These results are useful for applications in quantum information processing and also motivate further investigations, e.g., the use of an N -photon Jaynes-Cummings system as a qudit with harmonic spectrum and the exploration of multiphoton quantum interference.Introduction.-Recent technological advances in manipulating the radiation-matter interaction, especially at the level of a few atoms and photons, have allowed great strides in the implementation of quantum information processing protocols.The mastery of such interactions on various platforms [1][2][3][4][5] has made it possible to dispel mistrust regarding the possibility of a quantum computer becoming real [6]. Thus, one often sees new (or improved) quantum computing protocols being implemented on diverse setups [7][8][9][10][11][12][13].The most elementary interaction between atom and radiation was first described by Rabi in 1936 [14], considering the radiation as a classical field and a dipolar interaction. In its quantum version, it is possible to classify such a model into different regimes [15][16][17]. When the interaction energy is a small perturbation on the free energies, the quantum Rabi model can be reduced to the well-known Jaynes-Cummings (JC) model [18] through the rotating-wave approximation, which describes the usual coherent exchange of a quantum of energy between a two-level atom and a single-mode bosonic field.The JC model can be extended to nonlinear versions (nondipolar light-matter interaction) [19], in particular the multiphoton JC model [20,21] that considers multiphoton exchange. Such a nonlinear Hamiltonian appears, at least for two-photon interaction, in trapped-ion domain [22,23], optical [24] and microwave [25] cavities, or even in superconducting circuits [26][27][28][29][30]. In Refs. [29,30], a much more interesting scenario is presented since two-photon interactions can be impl...

Quantum Rabi–Stark model: solutions and exotic energy spectra

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Selective Interactions in the Quantum Rabi Model

“…the Rabi-Stark model, and show that the interplay between the Stark and Rabi couplings gives rise to selective k-photon interactions in the SC and USC regimes. Note that, previously, k-photon (or multi-photon) resonances have been investigated in the context of driven linear qubit-boson couplings [31][32][33][34][35][36], as well as with nonlinear couplings [37][38][39], and have recently found applications for quantum information science [40]. In our case, k-photon transitions appear as higher order processes of the linear QRM, while the Stark coupling is responsible for the selective nature of these interactions.…”

Radiation induced interaction potential of two qubits strongly coupled with a quantized electromagnetic field

“…Quantum Rabi model (QRM) describes the interaction of a two-level atom with a resonant single-mode quantum field in a cavity [1,2]. This model plays fundamental role in the radiation-matter interaction in cavity quantum electrodynamics [3][4][5], quantum optics [6], quantum information [7] and physics of condensed matter [8]. Recently, the model attracted attention due to the fact that in many systems it is possible [9,10] to control the interaction strength in a wide range, including the so called ultra strong coupling (USC) regime, which corresponds to the variation interval from 0.3 to 1.0 of a dimensionless coupling constant f between an atom (qubit) and a field.…”