Phys. Rev. Lett. 127, 183603 (2021)

Squeezed Lasing

Carlos Sánchez Muñoz and Dieter Jaksch

Phys. Rev. Lett. 127, 183603 – Published 29 October 2021

Abstract

We introduce the concept of a squeezed laser, in which a squeezed cavity mode develops a macroscopic photonic occupation due to stimulated emission. Above the lasing threshold, the emitted light retains both the spectral purity of a laser and the photon correlations characteristic of quadrature squeezing. Our proposal, implementable in optical setups, relies on a combination of the parametric driving of the cavity and the excitation by a broadband squeezed vacuum to achieve lasing behavior in a squeezed cavity mode. The squeezed laser can find applications that go beyond those of standard lasers thanks to the squeezed character, such as the direct application in Michelson interferometry beyond the standard quantum limit, or its use in atomic metrology.

Received 29 June 2021
Accepted 27 September 2021

DOI:https://doi.org/10.1103/PhysRevLett.127.183603

Physics Subject Headings (PhySH)

Lasers Photon pairs & parametric down-conversion Squeezing of quantum noise

Atomic systems

Atomic, Molecular & Optical

Authors & Affiliations

Carlos Sánchez Muñoz ^1,2,* and Dieter Jaksch^2,3

¹Departamento de Física Teórica de la Materia Condensada and Condensed Matter Physics Center (IFIMAC), Universidad Autónoma de Madrid, 28049 Madrid, Spain
²Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
³Institut für Laserphysik, Universität Hamburg, 22761 Hamburg, Germany

^*Corresponding author. carlossmwolff@gmail.com

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Vol. 127, Iss. 18 — 29 October 2021

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Figure 1
(a) Sketch of the proposed setup. A single cavity mode of frequency $ω_{c} = ω_{p} + Δ_{c}$ (with $Δ_{c} ≪ ω_{p}$ ) is parametrically driven through the down-conversion of pump photons of frequency $2 ω_{p}$ by a nonlinear crystal $χ^{(2)}$ . The cavity includes a gain medium (e.g., an ensemble of two-level atoms) and is driven by a broadband squeezed vacuum centered at the frequency $ω_{p}$ , which eliminates squeezedlike noise in the squeezed basis originating from cavity spontaneous emission. If the laser is imposed with a well-defined phase, the output emission corresponds to a coherent squeezed state of frequency $ω_{s} = ω_{p} + Δ_{s}$ . (b)–(c) Exact calculation of the Wigner function for the steady state in the lasing regime of (b) a standard laser ( $r = 0$ ) and (c) a squeezed laser ( $r = 1$ ), for $N = 1$ , $γ = 0$ , $C_{s} = 2$ , $n_{q} = 50$ , and $θ = π$ . For comparison, dashed lines mark the uncertainty contour of a vacuum state (b).
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Figure 2
Enforcing a well-defined phase. (a) Stationary photon population in the squeezed basis, compared with the square of the mean field, versus the amplitude of the coherent drive. Parameters, $n_{q} = 200$ ; $C = 2$ . (b) Wigner function of the steady state of the squeezed laser with a small seeding field. Dashed black lines are contour lines for $0.1 \max [W (x, p)]$ , blue dashed lines are the equivalent for a coherent field with the same coherent amplitude. Same parameters as in (a), and $r = 0.7$ . Seeding laser parameters, $n_{d} = 4 Ω^{2} / κ^{2} = 2$ ; $ϕ_{d} = 0$ . (c) Photon number distribution and (d) quadrature fluctuations versus the phase of the driving field, with the same parameters as in (b). Dashed line marks vacuum-level fluctuations. Squeezing is achieved with $ϕ_{d} = 0$ , $π$ .
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Figure 3
Line narrowing of the emission spectrum in a squeezed laser. (a) Emission linewidth (related to phase diffusion rate) versus cooperativity $C_{s} = p_{s}$ for different values of saturation photon number $n_{q}$ . The lasing phase transition occurs at $C_{s} = 1$ . This result depends on $r$ only through $C_{s}$ . (b) Spectrum versus cooperativity $C_{s}$ for saturation photon number $n_{q} = 100$ . Frequency defined with respect to the squeezed mode frequency $ω_{s}$ .
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Figure 4
Photon correlations of a squeezed laser. (a),(c) Squeezing spectrum versus time (negative values indicate fluctuations below the shot noise). (b),(c) Cuts of (a),(b) at initial and final time. We observe survival of squeezing for times much longer than cavity lifetime. Parameters, $n_{q} = 250$ ; $C_{s} = 2$ ; $φ = (θ + π) / 2$ ; $r = 0.45$ . (e) Evolution of normalized quadrature variance. (f) $g^{(2)} (τ)$ of the squeezed laser displaying positive correlations surviving for extremely long correlation times $\propto 1 / Γ$ , with $Γ \sim 0.1 κ$ in this particular case. A thermal state, shown for comparison, displays a much shorter positive correlation time of the order $1 / κ$ . Parameters, $C_{s} = 1.5$ ; $r = 1$ ; $n_{q} = 50$ .
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Physical Review Letters

Squeezed Lasing

Carlos Sánchez Muñoz and Dieter Jaksch

Phys. Rev. Lett. 127, 183603 – Published 29 October 2021

Abstract

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