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Physical Review A

Strongly quadrature-squeezed light from a single multilevel atom

Alex Elliott, A. S. Parkins

Published Apr 2, 2025• 0 citations
Publisher

Abstract

We propose schemes for steady-state emission of quadrature-squeezed light from a single-atom cavity quantum electrodynamics system. Two effective atom-cavity interaction models are suggested, motivated by correlated photon-pair emissions and multiphoton coherences that manifest themselves as squeezing of light emitted from the cavity. We consider idealized models to examine the mechanisms and optimal regimes for generating squeezed light. We also demonstrate realizations of these models based on both single $^{87}\mathrm{Rb}$ and $^{133}\mathrm{Cs}$ atoms, using combinations of laser- and laser-plus-cavity-driven Raman transitions between magnetic sublevels in a single ground hyperfine state. We show that these systems can in principle produce a much stronger level of squeezing than has previously been possible from a single-atom source.

DOI
10.1103/physreva.111.043703

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We propose schemes for steady-state emission of quadrature-squeezed light from a single-atom cavity quantum electrodynamics system. Two effective atom-cavity interaction models are suggested, motivated by correlated photon-pair emissions and multiphoton coherences that manifest themselves as squeezing of light emitted from the cavity. We consider idealized models to examine the mechanisms and optimal regimes for generating squeezed light. We also demonstrate realizations of these models based on both single 87Rb^{87}\mathrm{Rb}87Rb and 133Cs^{133}\mathrm{Cs}133Cs atoms, using combinations of laser- and laser-plus-cavity-driven Raman transitions between magnetic sublevels in a single ground hyperfine state. We show that these systems can in principle produce a much stronger level of squeezing than has previously been possible from a single-atom source.
We propose and investigate a scheme for the steady-state emission of quantum-correlated, telecom-band light from a single multilevel atom. By appropriately tuning the frequency of a pair of lasers, a two-photon transition is continually driven to an atomic excited state that emits photons at the desired wavelength. We show that resonantly coupling a cavity mode to the telecom transition can enhance the rate of emission while retaining the antibunched counting statistics that are characteristic of atomic light sources. We also explore coupling a second, independent cavity mode to the atom, which increases the telecom emission rate and introduces quantum correlations between the cavity modes. A model for the hyperfine structure of a single cesium atom is then described and numerically integrated to demonstrate the viability of implementing the scheme with a modern cavity QED system.
We consider a three-level cascade laser in which a coherently driven non-degenerate three-level atom available in a closed cavity coupled to a twomode vacuum reservoir.Applying the interaction Hamiltonian and Heisenberg equation of motion, we analyze the mean photon number, quadrature squeezing, and entanglement properties of the light produced by this quantum optical system inside the cavity.We find that the light generated by this system is in a two-mode squeezed state under certain conditions and the state of the system is weakly entangled at steady state due to the presence of the two-mode vacuum reservoir noise.
We analyze the quantum properties of the light generated by a three-level laser with an open cavity and coupled to a two-mode squeezed vacuum reservoir via a single-port mirror. The three-level laser consists of three-level atoms available in an open cavity and pumped from the bottom to the top level by means of electron bombardment. Applying the large-time approximation scheme, we have obtained the steady-state solutions of the equations of evolution for the expectation values of the atomic operators and the quantum Langevin equations for the cavity mode operators. Using the resulting steady-state solutions, we have calculated the mean photon number, the variance of the photon number, and the quadrature variance for the two-mode cavity light. We have seen that the light generated by the three-level laser is in a squeezed state and the squeezing occurs in the plus quadrature. It so turns out that the maximum quadrature squeezing of the two-mode cavity light is 45:68% for M0 = 0:59 and N0 = 0:27 below the vacuum-state level. In addition, we have shown that the effect of the squeezed parameter is to increase the mean and variance of the photon number.
We utilize multilevel atoms trapped in a driven resonant optical cavity to produce scalable multimode squeezed states for quantum sensing and metrology. While superradiance or collective dissipative emission by itself has been typically a detrimental effect for entanglement generation in optical cavities, in the presence of additional drives it can also be used as an entanglement resource. In a recent work [B. Sundar, D. Barberena, A. M. Rey, and A. Pi\~neiro Orioli, companion paper, Phys. Rev. Lett. 132, 033601 (2024)], we described a protocol for the dissipative generation of two-mode squeezing in the dark state of a six-level system with only one relevant polarization. There we showed that up to two quadratures can be squeezed. Here, we develop a generalized analytic treatment to calculate the squeezing in any multilevel system where atoms can collectively decay by emitting light into two polarization modes in a cavity. We show that in this more general system up to four spin squeezed quadratures can be obtained. We study how finite-size effects constrain the reachable squeezing, and analytically compute the scaling with NNN. Our findings are readily testable in current optical cavity experiments with alkaline-earth-like atoms.
We study the squeezing of output quadratures of an electro-magnetic field escaping from a resonator coupled to a general quantum system with arbitrary interaction strengths. The generalized theoretical analysis of output squeezing proposed here is valid for all the interaction regimes of cavity-quantum electrodynamics: from the weak to the strong, ultrastrong, and deep coupling regimes. For coupling rates comparable or larger then the cavity resonance frequency, the standard input–output theory for optical cavities fails to calculate the variance of output field-quadratures and predicts a non-negligible amount of output squeezing, even if the system is in its ground state. Here we show that, for arbitrary interaction strength and for general cavity-embedded quantum systems, no squeezing can be found in the output-field quadratures if the system is in its ground state. We also apply the proposed theoretical approach to study the output squeezing produced by: (i) an artificial two-level atom embedded in a coherently-excited cavity; and (ii) a cascade-type three-level system interacting with a cavity field mode. In the latter case the output squeezing arises from the virtual photons of the atom-cavity dressed states. This work extends the possibility of predicting and analyzing the results of continuous-variable optical quantum-state tomography when optical resonators interact very strongly with other quantum systems.
We have considered a cavity mode driven by coherent light and interacting with a three-level atom available in an open cavity coupled to a vacuum reservoir. We have carried out our analysis by putting the noise operators associated with the vacuum reservoir in normal order. We have also considered the interaction of the three-level atom with the vacuum reservoir outside the cavity. It is found that the squeezing occurs in both the plus and the minus quadratures and the maximum quadrature squeezing happens to be 52.08% and 33.32% below the vacuum state level, respectively. We have established that the uncertainty relation holds perfectly for this case as well. In addition, we have found that the squeezing in a pair of superposed cavity modes occurs in the plus and minus quadratures and have the same value. The amount of squeezing in each quadrature turns out to be half of the sum of the squeezing in the plus and minus quadratures of each cavity mode. Furthermore, we have observed that the presence of spontaneous emission decreases the mean photon number of the cavity mode but does not affect the maximum quadrature squeezing.