We present a Gaussian-state description of squeezed light generated in an optical parametric oscillator. Using the Gaussian-state description we describe the dynamics of the system conditioned on homodyne detection on the output field. Our theory shows that the output field is squeezed only if observed for long enough times or by a detector with finite bandwidth. As an application of the present approach we consider the use of finite bandwidth squeezed light together with a sample of spin-polarized atoms to estimate a magnetic field.
We present a Gaussian-state description of squeezed light generated in an optical parametric oscillator. Using the Gaussian-state description we describe the dynamics of the system conditioned on homodyne detection on the output field. Our theory shows that the output field is squeezed only if observed for long enough times or by a detector with finite bandwidth. As an application of the present approach we consider the use of finite bandwidth squeezed light together with a sample of spin-polarized atoms to estimate a magnetic field.
The Gaussian state description of continuous variables is adapted to describe the quantum interaction between macroscopic atomic samples and continuous-wave light beams. The formalism is very efficient: a non-linear differential equation for the covariance matrix of the atomic system explicitly accounts for both the unitary evolution, the dissipation and noise due to the atom-light interaction, and the back-action due to homodyne optical detection on the beam after its interaction with the atoms. Applications to atomic spin squeezing and estimation of unknown classical parameters are presented, and extensions beyond the Gaussian states are discussed.
Measurement of the squeezed fluctuations of an optical field by the method of conditional homodyne detection is discussed. It is shown that conditional homodyne detection is able to distinguish qualitatively between vacuum-state squeezing and squeezed classical noise. Whereas for conventional squeezed-light detection, only a quantitative distinction can be made, based on the setting of the shot-noise level, under conditional detection, the presence of classical noise changes the actual shape of the measured correlation function. The correlations show a positive peak due to the unsqeezed classical noise frequencies, set inside the negative dip associated with the squeezed fluctuations. The width in time of the positive peak is the larger of the detector response time and the inverse of the classical noise bandwidth. The fundamental distinction between vacuum-state squeezing and squeezed classical noise is that there is no positive peak, even in the limiting form of a delta-function, when the unsqueezed frequencies correspond to vacuum state modes. Implications for the literal interpretation of vacuum fluctuations, such as is adopted in stochastic electrodynamics, are discussed. The ideas are presented in general terms and illustrated by an example which treats the generation and detection of broadband squeezed light, including finite-bandwidth classical noise, within the framework of the quantum trajectory theory of cascaded open systems.
Squeezed states of the electromagnetic field are generated by degenerate parametric downconversion in a sub-threshold optical parametric oscillator. Reductions in photocurrent noise greater than 60% (−4 dB) below the limit set by the vacuum fluctuations of the field are observed in a balanced homodyne detector. A quantitative comparison with theory suggests that the observed noise reductions result from a field that in the absence of avoidable linear attenuation would be squeezed more than tenfold. A degree of squeezing of approximately fivefold is inferred for the actual field emitted through one mirror of the optical parametric oscillator. An explicit demonstration of the Heisenberg uncertainty principle for the electromagnetic field is made from the measurements, which show that the field state produced by the downconversion process is a state of minimum uncertainty.
A squeezed state of the electromagnetic field has less noise in one of its two amplitude components than that of a coherent state. This property makes squeezed states potentially useful in low noise and precision measurement. Squeezed states may be generated by, among other things, degenerate parametric amplifiers and four-wave mixers. The reduced noise in one of the amplitude components is most easily observed via a homodyne detector. A number of experimental efforts to generate and detect squeezed states are under way. Here, in describing experimental techniques, the experiments' carried out by Slusher et al. are emphasized. A number of techniques were employed to successfully generate squeezed light. An atomic beam of sodium provided the optical nonlinearity in a cavity-backward four-wave mixer. By employing pairs of Fabry-Perot modes spaced symmetrically about the pump frequency, squeezed light was generated in nondegenerate conditions where Rayleigh scattering of pump light could be avoided. To observe squeezing, a number of nonidealities such as phase jitter and detector inefficiencies also had to be overcome.
The quantum theory of photodetection is applied to the direct detection of multi-mode Gaussian-state light, with particular attention to the mean photocurrent and the photocurrent noise spectrum. Gaussian-state light comprises squeezed-state light plus additional classical Gaussian noise. By extending the familiar Gaussian moment-factoring formula of classical statistics to the antinormally ordered characteristic function of Gaussian-state light, the first and second moment photocurrent statistics for such illumination are shown to be completely characterized by knowledge of the mean function, the phase-sensitive correlation function, and the normally ordered correlation of the input light. The theory delineates the condition under which the strong-mean-field approximation is applicable to direct detection of such beams, i.e., it tells us when a direct detector yields the same noise spectrum as that of an in-phase homodyne detector. Numerical results are presented for the noise spectra of a squeezed amplifier, i.e., an optical parametric amplifier with signal-injection-induced gain saturation.
A synchronously pumped optical parametric oscillator (SPOPO) operating at 93 MHz is used to generate squeezed states at 1035 nm. The system features a counter-propagating beam at the same wavelength as the quantum state, which simultaneously actively stabilizes the cavity and, after transmission, acts as the local oscillator for homodyne detection. By deriving the local oscillator directly from the SPOPO cavity, the setup establishes an intrinsically excellent spatial mode overlap and high interference visibility, forming a distinctive self-referenced architecture. Two spatial light modulators enable precise spectral shaping of both the pump and the local oscillator in amplitude and phase, allowing investigation of the spectral properties of the generated states. The versatility of the setup further allows exploration of different SPOPO configurations, including regimes with varied finesse and escape efficiency. Representative measurements, including homodyne traces and squeezing levels as functions of pump power and local oscillator bandwidth, demonstrate the performance of the system. Theoretical simulations based on a multimode singular-value-decomposition model reproduce well the measured dependence of squeezing on pump power and LO bandwidth, confirming the accuracy of the description and the robustness of the setup. Measured squeezing levels up to − 3.3 dB are achieved, corresponding to − 5.7 dB at SPOPO output, evidencing the robustness and versatility of this platform for stable pulsed squeezed-light generation and advanced quantum optical applications.