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New Journal of Physics

Enhanced visibility of two-mode thermal squeezed states via degenerate parametric amplification and resonance

Imran Mahboob, Hajime Okamoto, Hiroshi Yamaguchi

Published Jul 29, 2016• 10 citations
Publisher

Abstract

Two-mode squeezed states, generated via non-degenerate parametric down-conversion, are invariably revealed via their entangled vacuum or correlated thermal fluctuations. Here, two-mode thermal squeezed states, generated in an electromechanical system, are made bright by means of degenerate parametric amplification of their constituent modes to the point where they are almost perfect, even when seeded from low intensity non-degenerate parametric down-conversion. More dramatically, activating the degenerate parametric resonances of the underlying modes yields perfect correlations which can be resolved via the coordinated switching of their phase bi-stable vibrations, without recourse to monitoring their thermal fluctuations. This ability to enhance the two-mode squeezed states and to decipher them without needing to observe their intrinsic noise is supported by both analytical and numerical modelling and it suggests that the technical constraints to making this phenomenon more widely available can be dramatically relaxed.

DOI
10.1088/1367-2630/18/8/083009

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Two-mode squeezed states, generated via non-degenerate parametric down-conversion, are invariably revealed via their entangled vacuum or correlated thermal fluctuations. Here, two-mode thermal squeezed states, generated in an electromechanical system, are made bright by means of degenerate parametric amplification of their constituent modes to the point where they are almost perfect, even when seeded from low intensity non-degenerate parametric down-conversion. More dramatically, activating the degenerate parametric resonances of the underlying modes yields perfect correlations which can be resolved via the coordinated switching of their phase bi-stable vibrations, without recourse to monitoring their thermal fluctuations. This ability to enhance the two-mode squeezed states and to decipher them without needing to observe their intrinsic noise is supported by both analytical and numerical modelling and it suggests that the technical constraints to making this phenomenon more widely available can be dramatically relaxed.
An electromechanical resonator is developed in which mechanical nonlinearities can be dynamically engineered to emulate the nondegenerate parametric down-conversion interaction. In this configuration, phonons are simultaneously generated in pairs in two macroscopic vibration modes, resulting in the amplification of their motion. In parallel, two-mode thermal squeezed states are also created, which exhibit fluctuations below the thermal motion of their constituent modes as well as harboring correlations between the modes that become almost perfect as their amplification is increased. The existence of correlations between two massive phonon ensembles paves the way towards an entangled macroscopic mechanical system at the single phonon level.
A mechanical resonator integrated with piezoelectric transducers enables mechanical nonlinearities to be dynamically engineered to emulate non-degenerate parametric down-conversion.In this configuration, millions of phonons are simultaneously generated in pairs in two macroscopic vibration modes, which results in the amplification of their motion by more than 20 dB.Mechanical two-mode squeezed states are also created in parallel, which exhibit fluctuations 5 dB below the thermal level of their constituent modes and they harbor correlations between the modes that become perfect as their amplification is increased.This remarkable observation of correlations between two massive phonon ensembles establishes the means to create an entangled macroscopic mechanical system at the single phonon level.
We investigate the statistical and quadrature squeezings, as well as the entanglement properties, of a two-mode light generated by non-degenerate parametric oscillations coupled to a two-mode squeezed vacuum reservoir, by employing the solutions of the quantum Langevin equations. It is found that the two-mode light shows the two-mode squeezing and entanglement for all values of the time. Moreover, it is observed that the squeezed vacuum reservoir and the growing amplitude of the pump mode enhance the degrees of two-mode squeezing and entanglement. We have also shown that the amounts of squeezing and entanglement are significant in a region, where the mean photon number is higher, and the photon number correlation is lower.
A degenerate optical parametric oscillator (DOPO) in the above threshold regime is a prominent source of squeezed field. In this study, a driven DOPO whose pump mode is coupled to a thermal bath while the signal mode is coupled to a squeezed vacuum reservoir is explored to understand the effect of the external squeezed light and the thermal fluctuations on the squeezing properties of both the intracavity and output pump and signal modes. Our findings showed that the injected squeezed vacuum reservoir enables the intracavity squeezing to surpass the maximum squeezing limit of 50% attainable in a DOPO coupled to an ordinary vacuum reservoir. We also found that the maximum squeezing of the output signal mode shifts from resonance to off-resonance in the presence of the injected squeezed vacuum field. Furthermore, the output pump mode exhibits nearly perfect squeezing for a squeezing parameter of r=2. Unlike the output signal mode, the maximum squeezing of the output pump mode occurs at resonance in the presence of the injected squeezed vacuum reservoir. Moreover, a considerable amount of squeezing is observed even in the presence of thermal fluctuations, as they are counterbalanced by the external squeezed light. Notably, relative damping rate between the pump and signal modes is observed to be a parameter that significantly influences squeezing, indicating the importance of optimizing the amount of damping depending on the intended purpose of the DOPO.
This thesis is primarily a theoretical study of degenerate parametric amplification as a means of generating squeezed-state light. i) A wideband traveling-wave formalism is developed for analyzing quantum mechanically a degenerate parametric amplifier. The formalism is based on spatial differential equations — spatial Langevin equations — that propagate temporal Fourier components of the field through the nonlinear medium. In addition to the parametric nonlinearity, the Langevin equations include absorption and associated fluctuations, dispersion, and pump quantum fluctuations. The dominant effects of dispersion and pump quantum fluctuations on the squeezing produced by a degenerate parametric amplifier are analyzed. ii) The wideband formalism of i) is used to carry out a more detailed analysis of the effects of phase mismatching. With the assumption of a lossless medium and a classical pump, we find that parametric amplification is capable of generating squeezed-state light over a wide band if materials with large χ(2) nonlinearities can be found, and that the squeezing bandwidth can be enhanced by phase mismatching away from degeneracy. iii) We consider again the effect of pump quantum fluctuations on the squeezing produced by parametric amplification. We perform discrete-mode calculations for a parametric amplifier with a quantum pump, and discuss some of the limitations of calculations of this sort in quantum optics. We derive stochastic differential equations (SDEs) for one- and two-mode parametric amplifiers, and from them obtain an iterative solution showing that pump quantum fluctuations impose a limitation on the degree of squeezing obtainable from a parametric amplifier. iv) A possible application of squeezing is considered; in particular, we study the effects of squeezing the intracavity noise in a laser oscillator. We solve the classical noise problem of a realistic laser model by making a bold — and possibly unrealizable — assumption, that the in-phase and quadrature Langevin sources which are responsible for the "noisiness" of the laser can be squeezed. We show that the effect of squeezing the in-phase quadrature is to reduce the phase noise, including the linewidth, of the laser but, due to amplitude-phase coupling, not to eliminate them altogether.
Quantum squeezing plays a crucial role in enhancing the precision of quantum metrology and improving the efficiency of quantum information processing protocols. We thus propose a scheme to amplify two-mode squeezing in nanomechanical resonators, harnessing parametric amplification and two-tone laser controls. The red-detuned laser drives facilitate the cooling of the nanomechanical resonators down to their ground state and allow optimal quantum state transfer in the weak-coupling, resolved sideband regime. In particular, the competing blue-detuned lasers in the driving pairs induce displacement squeezing in mechanical resonators. Thus, the quantum state transfer of the squeezing in nanomechanical resonators and the intracavity correlated photons of the parametric amplifier significantly enhance the two-mode mechanical squeezing. Notably, increasing the coupling strength of the red detuned laser and the ratio of blue-to-red detuned laser dramatically amplifies the two-mode mechanical squeezing under realistic experiment parameters of a typical optomechanical system. Our findings reveal that the proposed cooperative mechanism effectively enhances the level of two-mode mechanical squeezing with a considerable improvement and demonstrates exceptional resilience to thermal noise.