Ponderomotive Squeezing of Light by a Levitated Nanoparticle in Free Space

A mechanically compliant element can be set into motion by the interaction with light. In turn, this light-driven motion can give rise to ponderomotive correlations in the electromagnetic field. In optomechanical systems, cavities are often employed to enhance these correlations up to the point where they generate quantum squeezing of light. In free-space scenarios, where no cavity is used, observation of squeezing remains possible but challenging due to the weakness of the interaction, and has not been reported so far. Here, we measure the ponderomotively squeezed state of light scattered by a nanoparticle levitated in a free-space optical tweezer. We observe a reduction of the optical fluctuations by up to 25% below the vacuum level, in a bandwidth of about 15 kHz. Our results are explained well by a linearized dipole interaction between the nanoparticle and the electromagnetic continuum. These ponderomotive correlations open the door to quantum-enhanced sensing and metrology with levitated systems, such as force measurements below the standard quantum limit.

Figure 1

Free-space levitated optomechanics. (a) Experimental setup. (b) Power spectral density (PSD) of a phase quadrature measurement, normalized to the shot-noise (sn) background. (c) Sensitivity to mechanical motion, normalized to its maximum. The sensitivity is measured as the detector response to an off-resonant sinusoidal force acting on the particle. The light blue line is a sinusoidal fit.

Figure 2

Ponderomotive squeezing. Enlarged view of three different PSDs, at the phase quadrature (blue) and close to the amplitude one (red and green). The solid light-colored lines are the results of the fits to Eq. (5). The gray trace is the measured shot noise. We have subtracted from the PSDs a small classical noise contribution originating from the LO [30].

Figure 3

Homodyne tomography of ponderomotively squeezed light. (a),(b) Reconstructed Wigner functions of modes centered at, respectively, $\mathrm{\Omega }/(2\pi )=70.1\mathrm{kHz}$ and 77.1 kHz. The solid orange (dashed light gray) line indicates the covariance ellipse with 2 standard deviations of the squeezed (vacuum) state. Above and aside the Wigner functions we show the marginals distributions, $\rho$, for $X$ and $Y$, respectively. Blue dots are data; the dark gray lines are theoretical predictions [30]. The optical quadratures are normalized such that the vacuum noise standard deviation is $1/\sqrt{2}$.