Squeezing light with optomechanical and spin-light quantum interfaces

TL;DR

This work addresses realizing quantum-noise-limited light–matter interfaces and uses optical squeezing as a diagnostic of strong coupling. It develops a unified harmonic-oscillator framework and applies it to two experimental platforms: a spin ensemble and a membrane in a cavity, demonstrating polarization and ponderomotive squeezing with maximal quantum cooperativities of $C_{\mathrm{qu}}=10$ (spin) and $C_{\mathrm{qu}}=9$ (membrane). The observed squeezing, together with high cooperativities, confirms the quantum-nature of the light–matter interactions and supports long-distance, light-mediated coupling between disparate quantum systems. The results pave the way for hybrid quantum networks that enable quantum state transfer and entanglement between spin and mechanical degrees of freedom across macroscopic distances, including looped configurations that can cancel backaction and realize tunable $H_{\mathrm{hyb}}$ couplings.

Abstract

We investigate squeezing of light through quantum-noise-limited interactions with two different material systems: an ultracold atomic spin ensemble and a micromechanical membrane. Both systems feature a light-matter quantum interface that we exploit, respectively, to generate polarization squeezing of light through Faraday interaction with the collective atomic spin precession, and ponderomotive quadrature squeezing of light through radiation pressure interaction with the membrane vibrations in an optical cavity. Both experiments are described in a common theoretical framework, highlighting the conceptual similarities between them. The observation of squeezing certifies light-matter coupling with large quantum cooperativity, a prerequisite for applications in quantum science and technology. In our experiments, we obtain a maximal cooperativity of $C_\mathrm{qu} =10$ for the spin and $C_\mathrm{qu} = 9$ for the membrane. In particular, our results pave the way for hybrid quantum systems where spin and mechanical degrees of freedom are coherently coupled via light, enabling new protocols for quantum state transfer and entanglement generation over macroscopic distances.

Figures (5)

• Figure 1: Schematic of the light-matter quantum interfaces discussed in this paper: Coherent light interacts with a quantum system and is detected after the interaction. The quantum system is modeled as a harmonic oscillator of frequency $\Omega$, which is damped and stochastically driven through its coupling at rate $\gamma$ to a thermal environment. The light-matter interaction maps the $\hat{X}$ quadrature of the oscillator onto the $\hat{P}_L$-quadrature of the output light, while the $\hat{X}_L$-quadrature of the input light drives the oscillator, representing the measurement backaction. By adjusting the homodyne angle $\theta$, any superposition of the output light quadratures can be detected.
• Figure 2: Setup of the spin-light interface: The coherent input light is well polarised along $\bar{S}_x$. In this limit, the polarisation state of the light can be described in terms of harmonic oscillator quadratures $\hat{X}_L$ and $\hat{P}_L$. The light is focused on a pencil-shaped cloud of Rubidium atoms and interacts with the atomic spin via the Faraday interaction. Subsequently, the light is detected by polarisation homodyne detection using two waveplates and a polarizing beam-splitter (PBS). The quarter-wave plate (QWP) rotates the local oscillator onto the circular polarisation $\bar{S}_x \rightarrow \bar{S}_z$. The half-wave plate (HWP) is then used to set the homodyne angle $\theta$.
• Figure 3: (a) Variance of the polarisation fluctuations of the light after the interaction with the atoms. Here, the integration bandwidth is $f_\mathrm{bw} = \Delta_\mathrm{bw}/(2\pi) = 4kHz$, which is about an order of magnitude larger than the linewidth of the spin of $\gamma_{s} = 2\pi\times 280Hz$. The measurement rate is varied by changing the number of atoms in the dipole trap. Each data point is an average over ten measurements. The theory curve is calculated without free parameters, taking the inhomogeneous spin-light coupling into account, as described in the text, see Eq. \ref{['eq:spinVar']}. Here, the probe light is -30GHz red detuned and has a power of 1mW. The spin oscillator has a frequency of $\Omega_s = 2\pi\times0.98MHz$, set by a magnetic bias field of $B_x = 1.4G$. The detection efficiency of $\eta_\mathrm{det} = 0.83$ is included in the theory curve, which increases the effective shot noise contribution from $1$ to $1/\eta_\mathrm{det}$ (Eq. \ref{['eq:spinVar']} is modified accordingly). (b) Spectrum of the light around the spin resonance of $\Omega_s = 2\pi\times1.958MHz$ (magnetic bias field of $B_x = 2.8G$). Here, we detect at a homodyne angle of $\theta = 0.19\pi$. Polarization squeezing below the shot noise level is observed due to the quantum-noise limited interaction of the light with the atomic spin.
• Figure 4: The optomechanical interface: Coherent input light drives an optical cavity with a nanomechanical membrane inside, interacting with the membrane vibrations through radiation pressure. An image of the membrane (on top) and the vibration mode of the central defect (below) are shown as insets on the right. The light leaving the cavity is measured by homodyne detection. For this, it is combined with a local oscillator which is derived from the driving laser. The phase between the driving beam and the local oscillator can be controlled with a mirror glued on a piezo crystal. By changing this phase, any superposition between the amplitude quadrature $\hat{X}_L$ and the phase quadrature $\hat{P}_L$ of the output light can be detected.
• Figure 5: (a) Cavity dynamical backaction cooling experiment. The membrane phonon occupation is measured for a red-detuned light beam driving the cavity with different powers. Increasing the optical power decreases the phonon occupation due to thermal noise (dash-dotted line) but increases the contribution from backaction noise (dashed line). For large optical driving powers, the cooling and backaction driving effects balance and the membrane occupation approaches the theoretical limit of $n_{m} = 11$ phonons. The quantum cooperativity is unity for an input power of $224\,(20)µW$ and is about $C_m = 7.6\,(7)$ for the highest applied input power. (b) Spectrum of the light after the interaction with the membrane. The ponderomotive squeezing of the light shows up as a reduction of the noise below the shot noise floor shown in black. The blue line is a fit using Eq. \ref{['eq:fullPonderomotiveSqueezing']}. The fit yields a linewidth of $\gamma_{m,\mathrm{opt}} = 2\pi\times5.2kHz$ and a measurement rate of $\Gamma_m = 2\pi\times 47\,(2)kHz$, which gives a quantum cooperativity of $C_m = 9.0\,(4)$.