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New Journal of Physics

Spin two-axis-twisting via coherent population trapping based cavity QED

Liang Hu, Xiangming Hu, Junyu Chen, Jun Xu, Deyi Kong

Published Jun 1, 2023• 2 citations
Publisher

Abstract

Abstract We present a spin two-axis-twisting mechanism via coherent population trapping (CPT) based atom–photon interactions. CPT happens and the atoms are trapped in the dark state (coherent superposition of two ground states) when the ground states are resonantly coupled to a common excited state. Close to CPT, the atoms behave as two dark-state based spins, which interact with the common cavity vacuum fields. The otherwise nonexistent interaction is created between them and is identified to be responsible for the two-axis-twisting of the ground state spin. The essential difference from the previous schemes is the compatibility of the twisting spin squeezing with the resonant atom-light interaction. The CPT resonant unit serves as a kind of new ingredients for the quantum networks.

DOI
10.1088/1367-2630/acdb90

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Abstract We present a spin two-axis-twisting mechanism via coherent population trapping (CPT) based atom–photon interactions. CPT happens and the atoms are trapped in the dark state (coherent superposition of two ground states) when the ground states are resonantly coupled to a common excited state. Close to CPT, the atoms behave as two dark-state based spins, which interact with the common cavity vacuum fields. The otherwise nonexistent interaction is created between them and is identified to be responsible for the two-axis-twisting of the ground state spin. The essential difference from the previous schemes is the compatibility of the twisting spin squeezing with the resonant atom-light interaction. The CPT resonant unit serves as a kind of new ingredients for the quantum networks.
Spin twisting is generally not incompatible with steady-state atomic coherence because spin twisting as a representative kind of parametric processes is based on far-off-resonant atom-field interactions while the steady-state atomic coherence is achieved mainly by resonant interactions. Here we propose a resonant plus far-off-resonant scheme to generate the compatibility. The resonant part uses coherent population trapping (CPT) for steady-state maximal atomic coherence, while the far-off-resonant part utilizes Stark shift for a nonlinear response in analog with the motion of a cavity mirror under radiation pressure. The compatible combination CPT with the spin optodymanics analog to cavity optomechanics leads to the spin one- or two-axis-twisting together with steady-state maximal atomic coherence. The general conditions and the parameter regimes for the compatibility are analyzed. This scheme illustrates that the combination of CPT with Stark shift provides an efficient way for the compatibility of the spin twisting squeezing with steady-state maximal atomic coherence.
Spin squeezing has important applications in the field of quantum metrology and quantum information processing. Here we propose that coherent population trapping is well suitable for establishing cavity dissipation mechanism and generating a spin-squeezed state. An ensemble of N double Λ -type atoms is placed inside the two-mode optical cavity, where one Λ subsystem is driven resonantly by two strong control fields to form a dark resonance and the other Λ subsystem is coupled by two cavity vacuum fields and two external fields with large detunings. Due to the dark resonance, the atoms are trapped in a dark state and one has the maximal coherence between the two ground states. Two double off-resonance stimulated Raman scattering interactions are induced between fields and dressed atoms to establish a dissipative quantum dynamical process based on a collective cavity reservoir. As a result, strong stable spin squeezing is generated, which is verified by our numerical and analytical results. Published by the American Physical Society 2024
We present a scheme to generate unitarily two-mode and four-mode field squeezing in optical cavities with the near-resonantly dressed three-level atoms in the $\mathrm{\ensuremath{\Lambda}}$ configuration. The dressing fields open two coherent population trapping (CPT) windows, within which the atoms stay predominantly in the dark state and yield strong nonlinearities for both the dressing fields themselves and the other applied fields. The two-mode squeeze operator is separated from degrees of freedom of atoms in a common CPT window, and the multimode squeeze operator is segregated in different CPT windows. The resulting two-mode and multimode interaction strengths are at least one order higher than in the previous dispersive schemes, where all fields are far off resonant with the atoms. The present near-resonant scheme is robust to spontaneous emission since atoms are nearly trapped in a long-lived superposition state.
We investigate the generation of entanglement (spin squeezing) in an optical-transition atomic clock through the coupling to an optical cavity in its vacuum state. We show that if each atom is prepared in a superposition of the ground state and a long-lived electronic excited state, and viewed as a spin-1/2 system, then the collective vacuum light shift entangles the atoms, resulting in a squeezed distribution of the ensemble collective spin, without any light applied. This scheme reveals that even an electromagnetic vacuum can constitute a useful resource for entanglement and quantum manipulation. By rotating the spin direction while coupling to the vacuum, the scheme can be extended to implement two-axis twisting resulting in stronger squeezing.
The coherent population trapping (CPT) under resonance interaction of elliptically polarized light, with atoms having degenerated energy levels, is analytically treated in an invariant way, without using a specific coordinate frame. Tensors describing dark states are found in an explicit and invariant form for all atomic transitions, where CPT takes place. The correspondence between elliptical polarization vectors and pairs of unit spinors is established. It is shown that all dark states in the problem under consideration, can be constructed from these spinors, by taking multiple tensor products. In the case of an integer angular momentum, this general construction is reduced to a multiple tensor product of vectors. A general significance and some applications of these results are indicted.