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Laser Physics Letters

Multiphoton processes between one atom and a multimode field

Lü-Yun Cheng, Zi‐Liang Lan, Sai-Yun Ye, Zhi‐Rong Zhong

Published Jun 1, 2025• 0 citations
Publisher

Abstract

Abstract In this paper, we present a theoretical investigation of multiphoton processes between a single atom and a multimode optical or microwave field. At first, we examine two-photon excitation, which involves the simultaneous excitation of two photons in different cavity modes by a single atom. We demonstrate that when the transition frequency of an atom is equal to the sum of the frequencies of two cavity modes, there exists a resonant coupling between the atom and the two-mode cavity field, which leads to the simultaneous excitation of the two cavity photons with the atom initially in its excited state. Moreover, we found that this coupling is coherent and reversible, allowing the atom initially in the ground state to simultaneously absorb all the photons from the cavities and transit to its excited state. Finally, we also show that this coherent interaction, in principle, can be extended to describe multiphoton processes between a single atom and a multimode cavity field, such as a three-mode cavity. The parameters used in the numerical simulation are based on the experimentally demonstrated values in circuit quantum electrodynamics systems.

DOI
10.1088/1612-202x/addd85

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Abstract In this paper, we present a theoretical investigation of multiphoton processes between a single atom and a multimode optical or microwave field. At first, we examine two-photon excitation, which involves the simultaneous excitation of two photons in different cavity modes by a single atom. We demonstrate that when the transition frequency of an atom is equal to the sum of the frequencies of two cavity modes, there exists a resonant coupling between the atom and the two-mode cavity field, which leads to the simultaneous excitation of the two cavity photons with the atom initially in its excited state. Moreover, we found that this coupling is coherent and reversible, allowing the atom initially in the ground state to simultaneously absorb all the photons from the cavities and transit to its excited state. Finally, we also show that this coherent interaction, in principle, can be extended to describe multiphoton processes between a single atom and a multimode cavity field, such as a three-mode cavity. The parameters used in the numerical simulation are based on the experimentally demonstrated values in circuit quantum electrodynamics systems.
We consider two separate atoms interacting with a single-mode optical or microwave resonator. When the frequency of the resonator field is twice the atomic transition frequency, we show that there exists a resonant coupling between one photon and two atoms, via intermediate virtual states connected by counterrotating processes. If the resonator is prepared in its one-photon state, the photon can be jointly absorbed by the two atoms in their ground state which will both reach their excited state with a probability close to one. Like ordinary quantum Rabi oscillations, this process is coherent and reversible, so that two atoms in their excited state will undergo a downward transition jointly emitting a single cavity photon. This joint absorption and emission process can also occur with three atoms. The parameters used to investigate this process correspond to experimentally demonstrated values in circuit quantum electrodynamics systems.
We consider two separate atoms interacting with a single-mode optical resonator. When the frequency of the resonator field is twice the atomic transition frequency, we show that there exists a resonant coupling between one photon and two atoms, via intermediate virtual states connected by counter-rotating processes. If the resonator is prepared in its one-photon state, the photon can be jointly absorbed by the two atoms in their ground state which will both reach their excited state with probability close to one. Like ordinary quantum Rabi oscillations, this process is coherent and reversible, so that two atoms in their excited state will undergo a downward transition jointly emitting a single cavity photon. This joint absorption and emission processes can also occur with three atoms. The parameters used to investigate this process correspond to experimentally demonstrated values in circuit quantum electrodynamics systems.
When an atom is strongly coupled to a cavity, the two systems can exchange a single photon through a coherent Rabi oscillation. This process enables precise quantum-state engineering and manipulation of atoms and photons in a cavity, which play a central role in quantum information and measurement. Recently, a new regime of cavity QED was reached experimentally where the strength of the interaction between light and artificial atoms (qubits) becomes comparable to the atomic transition frequency or the resonance frequency of the cavity mode. Here we show that this regime can strongly modify the concept of vacuum Rabi oscillations, enabling multiphoton exchanges between the qubit and the resonator. We find that experimental state-of-the-art circuit-QED systems can undergo two- and three-photon vacuum Rabi oscillations. These anomalous Rabi oscillations can be exploited for the realization of efficient Fock-state sources of light and complex entangled states of qubits.
We investigate the multiphoton quantum dynamics of a leaking single-mode quantized cavity field coupled with a resonantly driven two-level system possessing permanent dipoles. The frequencies of the interacting subsystems being considered are very different, e.g., the microwave range for the cavity and the optical domain for the frequency of the two-level emitter, respectively. In this way, the emitter couples to the resonator mode only via its diagonal dipole moments. Furthermore, the generalized Rabi frequency resulting from the external coherent driving of the two-level subsystem is also assumed to be different from the resonator's frequency or its multiples. As a consequence, this highly dispersive interaction regime is responsible for the cavity multiphoton quantum dynamics and photon conversion from the optical to microwave range, respectively.
We theoretically investigate quantum Rabi oscillations in a system consisting of a two-level atom (qubit) strongly coupled to a one-dimensional open waveguide. In contrast to conventional cavity quantum electrodynamics, the qubit interacts with a continuum of propagating modes, which gives rise to fundamentally different dynamical behavior. Within the rotating-wave approximation, we express the multimode Jaynes-Cummings Hamiltonian in terms of collective bosonic operators and show that the system possesses two integrals of motion, enabling an exact diagonalization of the Hamiltonian in the single-excitation subspace. We show that for a strongly interacting qubit-photon system, the dynamics are captured by a reduced two-level model. In this framework, each level is defined as the product of the atomic excited state and a specific field mode, which takes the form of a multiphoton Fock-like state. In this picture, the Rabi oscillations represent a collective phenomenon corresponding to oscillations between multiphoton states differing by a single photon. We then extend our analysis to multiphoton processes in which the initial field is a coherent state with a continuous spectrum. In this case, the Rabi frequency is shown to be sensitive to the spectral profile of the function that generates the coherent state.
We study the dynamics of a system composed of two coupled cavities, each interacting with a single Rydberg atom. The interplay between Rydberg-Rydberg interaction and photon hopping enables the transition of the atoms from the collective ground state to the double Rydberg excitation state by individually interacting with the optical normal modes and suppressing the upconversion process between them. The atomic transition is accompanied by the two-photon absorption and emission of the normal modes. Since the energy level structure of the atom-cavity system is photon number dependent there is only a pair of states being in the two-photon resonance. Therefore, the system can act as a quantum nonlinear absorption filter through the nonclassical quantum process, converting coherent light field into a nonclassical state. Meanwhile, the vacuum field in the cavity inspires the Rydberg atoms to simultaneously emit two photons into the normal mode, resulting in obvious emission enhancement of the mode.