Achievable Squeezing Research Articles

Squeezing below the ground state of motion of a continuously monitored levitating nanoparticle

Abstract Squeezing is a crucial resource for quantum information processing and quantum sensing. In levitated nanomechanics, squeezed states of motion can be generated via temporal control of the trapping frequency of a massive particle. However, the amount of achievable squeezing typically suffers from detrimental environmental effects. We propose a scheme for the generation of significant levels of mechanical squeezing in the motional state of a levitated nanoparticle by leveraging on the careful temporal control of the trapping potential. We analyse the performance of such a scheme by fully accounting for the most relevant sources of noise, including measurement backaction. The feasibility of our proposal, which is close to experimental state-of-the-art, makes it a valuable tool for quantum state engineering.

Distillation of squeezing using an engineered pulsed parametric down-conversion source.

Hybrid quantum information processing combines the advantages of discrete and continues variable protocols by realizing protocols consisting of photon counting and homodyne measurements. However, the mode structure of pulsed sources and the properties of the detection schemes often require the use of optical filters in order to combine both detection methods in a common experiment. This limits the efficiency and the overall achievable squeezing of the experiment. In our work, we use photon subtraction to implement the distillation of pulsed squeezed states originating from a genuinely spatially and temporally single-mode parametric down-conversion source in non-linear waveguides. Due to the distillation, we witness an improvement of 0.17 dB from an initial squeezing value of -1.648 ± 0.002 dB, while achieving a purity of 0.58, and confirm the non-Gaussianity of the distilled state via the higher-order cumulants. With this, we demonstrate the source's suitability for scalable hybrid quantum network applications with pulsed quantum light.

Mechanical squeezing in a dissipative optomechanical system with an optical parametric amplifier

We theoretically demonstrate that an especially tuned degenerate optical parametric amplifier (OPA) inside a cavity can lead to the momentum squeezing of a moving membrane in a dissipative optomechanical system. The momentum squeezing of the membrane depends on the parametric gain and the parametric phase of the OPA, the power of the external laser driving the cavity, and the temperature of the environment. The best achievable momentum squeezing is about 2.53 dB, which is limited by the OPA. Moreover, we show that the momentum squeezing of the membrane can be detected by directly measuring the cavity output field. In addition, we find that the mechanical squeezing can be enhanced to about 10.36 dB under the joint effect of the OPA and an input broadband squeezed vacuum field.

Time-domain analysis on the pulsed squeezed vacuum detected with picosecond pulses

The pulsed squeezed state of light is expected to enhance the sensitivity of optical measurements using optical pulses. To achieve a high squeezing level, it is crucial to explore its limiting factors. In this study, we analyze the pulsed squeezed vacuum detected with picosecond pulses to explore two critical factors that limit the achievable squeezing level. First, we investigate the effect of the frequency chirp of local oscillator (LO) pulses and show that there exists an upper bound of the chirp parameter for a given squeezing level. Next, we analyze the effect of temporal matching between the LO pulse and the squeezed vacuum and point out the importance of temporal broadening in nonlinear optical crystals for squeezing.

Robust Spin Squeezing via Photon-Mediated Interactions on an Optical Clock Transition.

Cavity QED is a promising avenue for the deterministic generation of entangled and spin-squeezed states for quantum metrology. One archetypal scheme generates squeezing via collective one-axis twisting interactions. However, we show that in implementations using optical transitions in long-lived atoms the achievable squeezing is fundamentally limited by collectively enhanced emission into the cavity mode which is generated in parallel with the cavity-mediated spin-spin interactions. We propose an alternative scheme which generates a squeezed state that is protected from collective emission, and investigate its sensitivity to realistic sources of experimental noise and imperfections.

Harnessing temporal modes for multi-photon quantum information processing based on integrated optics.

In the last few decades, there has been much progress on low loss waveguides, very efficient photon-number detectors and nonlinear processes. Engineered sum-frequency conversion is now at a stage where it allows operation on arbitrary temporal broadband modes, thus making the spectral degree of freedom accessible for information coding. Hereby the information is often encoded into the temporal modes of a single photon. Here, we analyse the prospect of using multi-photon states or squeezed states in different temporal modes based on integrated optics devices. We describe an analogy between mode-selective sum-frequency conversion and a network of spatial beam splitters. Furthermore, we analyse the limits on the achievable squeezing in waveguides with current technology and the loss limits in the conversion process.This article is part of the themed issue 'Quantum technology for the 21st century'.

Deep feedback-stabilized parametric squeezing in an opto-electromechanical system

Using a stabilizing quadrature-feedback scheme the thermal motion of an on-chip opto-electromechanical resonator is squeezed far beyond the limit of classical parametric squeezing. It is shown that feedback on the Y quadrature by itself can already squeeze the thermal motion of the resonator, but the maximum achievable squeezing level is limited by the imprecision noise. By combining the feedback and parametric pumping a record of 15.1 dB of classical noise squeezing is demonstrated. This not only largely exceeds the 3 dB limit for regular squeezing, but is also deeper than ever can be achieved with feedback cooling. The detector-resonator interaction is analyzed within the semi-classical framework and it is shown that using this feedback-stabilized parametric pumping technique true quantum-squeezed states can be prepared when the resonator starts off close to its ground state, and that the ultimate amount of squeezing depends on the minimum detuning that can be achieved.

Quantum filtering of a thermal master equation with a purified reservoir

We consider a system subject to a quantum optical master equation at finite temperature and study a class of conditional dynamics obtained by monitoring its totally or partially purified environment. More specifically, drawing from the notion that the thermal state of the environment may be regarded as the local state of a lossy and noisy two-mode squeezed state, we consider conditional dynamics ("unravellings") resulting from the homodyne detection of the two modes of such a state. Thus, we identify a class of unravellings parametrised by the loss rate suffered by the environmental two-mode state, which interpolate between direct detection of the environmental mode alone (occurring for total loss, whereby no correlation between the two environmental modes is left) and full access to the purification of the bath (occurring when no loss is acting and the two-mode state of the environment is pure). We hence show that, while direct detection of the bath is not able to reach the maximal steady-state squeezing allowed by general-dyne unravellings, such optimal values can be obtained when a fully purified bath is accessible. More generally we show that, within our framework, any degree of access to the bath purification improves the performance of filtering protocols in terms of achievable squeezing and entanglement.

Planar squeezing by quantum non-demolition measurement in cold atomic ensembles

Planar squeezed states, i.e. quantum states which are squeezed in two orthogonal spin components, have recently attracted attention due to their applications in atomic interferometry and quantum information (He et al 2012 New J. Phys. 14 093012). While canonical variables such as quadratures of the radiation field can be squeezed in at most one component, simultaneous squeezing in two orthogonal spin components can be achieved due to the angular momentum commutation relations. We present a novel scheme for planar squeezing via quantum non-demolition (QND) measurements in spin-1 systems. The QND measurement is achieved via near-resonant paramagnetic Faraday rotation probing, and the planar squeezing is obtained by sequential QND measurement of two orthogonal spin components. We compute the achievable squeezing for a variety of optical depths, initial conditions and probing strategies. The planar squeezed states generated in this way contain entanglement detectable by spin-squeezing inequalities and give an advantage relative to non-squeezed states for any precession phase angle, a benefit for single-shot and high-bandwidth magnetometry.

Spin squeezing of one-axis twisting model in the presence of phase dephasing

We present a detailed analysis of spin squeezing of the one-axis twisting model with a many-body phase dephasing, which is induced by external field fluctuation in a two-mode Bose-Einstein condensates. Even in the presence of the dephasing, our analytical results show that the optimal initial state corresponds to a coherent spin state $|\theta_{0}, \phi_0\rangle$ with the polar angle $\theta_0=\pi/2$. If the dephasing rate $\gamma\ll S^{-1/3}$, where $S$ is total atomic spin, we find that the smallest value of squeezing parameter (i.e., the strongest squeezing) obeys the same scaling with the ideal one-axis twisting case, namely $\xi^2\propto S^{-2/3}$. While for a moderate dephasing, the achievable squeezing obeys the power rule $S^{-2/5}$, which is slightly worse than the ideal case. When the dephasing rate $\gamma>S^{1/2}$, we show that the squeezing is weak and neglectable.

Generation of mechanical squeezing via magnetic dipoles on cantilevers

A scheme to squeeze the center-of-mass motional quadratures of a quantum mechanical oscillator below its standard quantum limit is proposed and analyzed theoretically. It relies on the dipole-dipole coupling between a magnetic dipole mounted on the tip of a cantilever to equally oriented dipoles located on a mesoscopic tuning fork. We also investigate the influence of several sources of noise on the achievable squeezing, including classical noise in the driving fork and the clamping noise in the oscillator. A detection of the state of the cantilever based on state transfer to a light field is considered. We investigate possible limitations of that scheme.

Critical Kerr nonlinear optical cavity in the presence of internal loss and driving noise

We theoretically analyze the noise transformation of a high-power continuous-wave light field that is reflected off a critical Kerr nonlinear cavity (KNLC). Our investigations are based on a rigorous treatment in the time domain. Thereby, realistic conditions of a specific experimental environment including optical intracavity loss and strong classical driving noise can be modeled for any KNLC. We show that, even in the presence of optical loss and driving noise, considerable squeezing levels can be achieved. We find that the achievable squeezing levels are not limited by the driving noise but solely by the amount of optical loss. Amplitude-quadrature squeezing of the reflected mean field is obtained if the KNLC's operating point is chosen properly. Consistently, a KNLC can provide a passive purely optical reduction of laser-power noise as experimentally demonstrated in Khalaidovski et al. [Phys. Rev. A 80, 053801 (2009)]. We apply our model to this experiment and find good agreement with measured noise spectra.

Field dispersion in parametrically excited oscillator upon relaxation

A complete system of solutions of the equation describing the parametric excitation of an oscillator is presented. This system makes it possible to take into account losses in a parametrically excited oscillator in terms of the perturbation theory. It is shown that, although the oscillator losses are small (the relative spectral width of a typical laser cavity is 10−8), they limit the achievable squeezing coefficients by values on the order of ten. At present, the progress in resonator technique allows one to achieve relative spectral widths on the order of 10−11–10−12. Therefore, it can be expected to achieve squeezing coefficients on the order of 103.

Light Squeezing in a Fabry–Perot Cavity

A quantum mechanical model for the study of quadrature squeezing in radiation coming out of Fabry–Perot cavity containing nonlinear Kerr medium has been proposed. We have incorporated the vacuum fluctuations entering in the cavity through unused ports. The analysis has been applied to a sample of GaAs filled in the Fabry–Perot cavity and irradiated by an off-resonant Co:MgF2 laser. Limitations on achievable squeezing due to incident pump power, interaction time, nonlinear coupling parameter and facet reflectivities have been discussed and it is seen that low reflectivity of front facet and high reflectivity of rear facet of the cavity produces substantial squeezing.

Targeting steady states in a laser

The targeting method recently proposed by Lippi et al. to shorten lengthy transients in separable systems has been experimentally implemented in the particular case of a solid-state laser. It allows to reduce the intensity transient of a Nd{sup 3+}:YVO{sub 4} laser by a factor of 60 and its duration by a factor in excess of 10 without altering the system. This process is extremely sensitive to targeting parameters due to the stiffness of the system. Internal noise sets a practical limit on the achievable squeezing of transients.

Squeezed Cascade Two-Quantum-Beat Lasers

Noise squeezing of intensity difference between the pair of sum modes may be generated in a cascade laser of Λ and V quantum-beats. The best achievable squeezing is up to 50% below the shot noise limit. This new kind of squeezed lasers has potential for quantum communications and precision measurements.

Impacts of the self-Raman effect and third-order dispersion on pulse-squeezed state generation using optical fibers

Based on a newly developed general quantum theory of nonlinear optical pulse propagation, the influences of the self-Raman effect and third-order dispersion on the achievable squeezing ratio in squeezing experiments with optical fibers at both the 1.3- and 1.55-μm wavelengths are studied. In the presence of these effects, squeezing still survives, but the achievable squeezing will reach a limit as the propagation distance increases. Temperature dependence of the squeezing ratio is also examined.

Squeezing in the Jaynes-Cummings model for Large Coherent Fields

Abstract We use the recently-established asymptotic solution (AS) for large fields to study squeezing in the Jaynes-Cummings model. Arbitrary initial atomic states (including atomic coherence) are considered. We find that most features of squeezing can be understood from the properties of the asymptotic field states, and from the observation, which we establish numerically, that for large fields the interference between the two branches of the wavefunction does not contribute significantly to the squeezing (not even near the revival times, when the two field states being superposed have very nearly the same phase). We obtain a limit on the time over which the field may show any squeezing and find that it scales as the 3/4 power of the number of photons. We also obtain a bound on the maximum achievable squeezing for a given number of photons, which is an improvement over earlier estimates. Finally, we discuss some of the shortcomings of the AS, and in particular the existence of a small ghost peak in the f...

Higher-order squeezing in three- and four-wave mixing processes with loss.

An investigation is carried out of higher-order squeezing in a class of three- and four-wave mixing processes that can be modeled by a master equation. In (2N)th-order squeezing, as defined by Hong and Mandel, the Nth-power of the variance of a field quadrature falls below the value it would have for a coherent state. Higher-order squeezing is of interest because (i) it occurs in many processes in which ordinary (or second-order) squeezing occurs, and (ii) it allows a much larger fractional noise reduction to be achieved than ordinary squeezing. The master equation we use models a degenerate three- or four-wave process and takes into account the losses in the signal mode. We convert the master equation into a Fokker-Planck equation for the Wigner distribution function and solve it for a wide range of initial signal states (including thermal, coherent, Fock states, and mixtures of these). Results are presented for the enhancement of fourth- and sixth-order squeezing over second-order squeezing. Differences in the character of higher-order squeezing for different input states are pointed out. The role of losses in limiting the amount of achievable squeezing in all orders is especially investigated.

GENERATION OF SQUEEZED LIGHT IN IDEAL CAVITY BY INJECTING ATOMS

Two level atoms are injected into ideal cavity one by one to interact with the light field therein which intially is in coherent state. In one-photon transition case, the quadrature variance could be reduced by this means for suitably chosen interaction time t. But there exists some limitation, the squeezing will become worse if the number of times K is too large. In twophoton transition case, for large mean photon tumber N and optimum interaction time t = π/ g2, analytical formula for dependence of quadrature variance on N and K can be obtained. This formula shows that deep squeezing can be achieved by suitably chosen K. And the larger the N is, the stronger the achievable squeezing will be.