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arXiv:1305.2351 · Physical Review A

Two-photon absorption and emission by Rydberg atoms in coupled cavities

Huai‐Zhi Wu, Zhen‐Biao Yang, Shi‐Biao Zheng

Published Oct 10, 2013• 11 citations
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Abstract

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.

DOI
10.1103/physreva.88.043816

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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.
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.
Enhanced two-photon decay has been observed for the first time in an electric dipole transition between two Rydberg levels coupled to a single mode of a strongly driven microwave cavity. This was achieved by dynamically suppressing the otherwise dominant single-photon decay. The experiment is compared with a dressed-state model which treats the external driving field exactly. Cavity-induced emission and absorption rates are calculated to fourth order in the interaction to include two-photon processes, and are found to fit the experimental data well.
The realization of a Jaynes-Cummings model in the optical domain is proposed for an atomic ensemble. The scheme exploits the collective coupling of the atoms to a quantized cavity mode and the nonlinearity introduced by coupling to high-lying Rydberg states. A two-photon transition resonantly couples the single-atom ground state $|g\ensuremath{\rangle}$ to a Rydberg state $|e\ensuremath{\rangle}$ via a nonresonant intermediate state $|i\ensuremath{\rangle}$, but due to the interaction between Rydberg atoms only a single atom can be resonantly excited in the ensemble. This restricts the state space of the ensemble to the collective ground state $|G\ensuremath{\rangle}$ and the collectively excited state $|E\ensuremath{\rangle}$ with a single Rydberg excitation distributed evenly on all atoms. The collectively enhanced coupling of all atoms to the cavity field with coherent coupling strengths which are much larger than the decay rates in the system leads to the strong coupling regime of the resulting effective Jaynes-Cummings model. We use numerical simulations to show that the cavity transmission can be used to reveal detailed properties of the Jaynes-Cummings ladder of excited states and that the atomic nonlinearity gives rise to highly nontrivial photon emission from the cavity. Finally, we suggest that the absence of interactions between remote Rydberg atoms may, due to a combinatorial effect, induce a cavity-assisted excitation blockade whose range is larger than the typical Rydberg dipole-dipole interaction length.
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.
The quantum dynamics of a hyper-Raman coupled model interacting with two modes of the quantized cavity field is described. The model consists of a four-level atom in a v configuration where transitions between the ground and excited states occur through the absorption (emission) of two photons from one mode and the emission (absorption) of one photon from the other and where two intermediate states are taken to be far off-resonance and are adiabatically removed. This is a multiphoton extension of the Jaynes-Cummings model and is exactly solvable. We study the atomic inversion and investigate the production of non-classical light exhibiting antibunching, violations of the Cauchy-Schwartz inequality, and squeezing.