Entanglement in the above-threshold optical parametric oscillator
Alessandro S. Villar, Katiuscia N. Cassemiro, Kaled Dechoum, Antonio Z. Khoury, Marcelo Martinelli, Paulo Nussenzveig
备注：
9 pages, 6 figs. Important reference for readers of quant-ph/0610197. J. Opt. Soc. Am. B, Feature Issue on Optical Quantum-Information Science, doc. ID 70938 (posted 5 September 2006, in press)
We investigate entanglement in the above-threshold Optical Parametric Oscillator, both theoretically and experimentally, and discuss its potential applications to quantum information. The fluctuations measured in the subtraction of signal and idler amplitude quadratures are $Δ^2 \hat p_-=0.50(1)$, or $-3.01(9)$ dB, and in the sum of phase quadratures are $Δ^2 \hatq_+=0.73(1)$, or $-1.37(6)$ dB. A detailed experimental study of the noise behavior as a function of pump power is presented, and discrepancies with theory are discussed.
We study microwave response of a Josephson parametric oscillator consisting of a superconducting transmission-line resonator with an embedded dc-SQUID. The dc-SQUID allows to control the magnitude of a Kerr nonlinearity over the ranges where it is smaller or larger than the photon loss rate. Spectroscopy measurements reveal the change of the microwave response from a classical Duffing oscillator to a Kerr parametric oscillator in a single device. In the single-photon Kerr regime, we observe parametric oscillations with a well-defined phase of either $0$ or $π$, whose probability can be control…
Glauber coherent states of quantum systems are reviewed. We construct the tomographic probability distributions of the oscillator states. The possibility to describe quantum states by tomographic probability distributions (tomograms) is presented on an example of coherent states of parametric oscillator. The integrals of motion linear in the position and momentum are used to explicitly obtain the tomogram evolution expressed in terms of trajectories of classical parametric oscillator
The dynamics of mixedness and entanglement is examined by solving the time-dependent Schrödinger equation for three coupled harmonic oscillator system with arbitrary time-dependent frequency and coupling constants parameters. We assume that part of oscillators is inaccessible and remaining oscillators accessible. We compute the dynamics of entanglement between inaccessible and accessible oscillators. In order to show the dynamics pictorially we introduce three quenched models. In the quenched models both mixedness and entanglement exhibit oscillatory behavior in time with multi-frequencies. It…
We apply the Walborn [Walborn S P, Taketani B G, Salles A, Toscano F and de Matos Filho R L 2009 Entropic Entanglement Criteria for Continuous Variables Phys. Rev. Lett. 103 160505] Shannon Entropic Entanglement Criterion (SEEC), to simple harmonic oscillators, a system typically discussed in undergraduate quantum mechanics courses. In particular, we investigate the entanglement of a system of coupled harmonic oscillators. A simple form of entanglement criterion in terms of their interaction is found. It is shown that a pair of interacting ground state coupled oscillators are more likely to be…
We study the dissipative dynamics of a single quantum harmonic oscillator subjected to a parametric driving with in an effective Hamiltonian approach. Using Liouville von Neumann approach, we show that the time evolution of a parametrically driven dissipative quantum oscillator has a strong connection with the classical damped Mathieu equation. Based on the numerical analysis of the Monodromy matrix, we demonstrate that the dynamical instability generated by the parametric driving are reduced by the effect of dissipation. Further, we obtain a closed relationship between the localization of the…
New families of time-dependent potentials related to the parametric oscillator are introduced. This is achieved by introducing some general time-dependent operators that factorize the appropriate constant of motion (quantum invariant) of the parametric oscillator, leading to new families of quantum invariants that are almost-isospectral to the initial one. Then, the respective time-dependent Hamiltonians are constructed, and the solutions of the Schrödinger equation are determined from the intertwining relationships and by finding the appropriate time-dependent complex-phases of the Lewis-Ries…
We use a versatile model to evaluate the multipartite entanglement and the nonclassical light generation in optical parametric oscillators, exploring the differences between doubly and triply resonant cavity configurations. We demonstrate the entanglement of the pump mode with converted fields in both situations, and the fundamental differences of oscillators using parametric down conversion and four wave mixing processes as the intracavity amplification technique. The strong correlations involving the sidebands of the pump and converted fields gives the signatures of a rich dynamic of multipa…
Generation of squeezed light with monolithic optical parametric oscillator: Simultaneous achievement of phase matching and cavity resonance by temperature control
In this work we study the production and swapping of non-gaussian multipartite entanglement in a setup containing a parametric amplifier which generates three photons in different modes coupled to three qubits. We prove that the entanglement generated in this setup is of nongaussian nature. We introduce witnesses of genuine tripartite nongaussian entanglement, valid both for mode and qubit entanglement. Moreover, those witnesses show that the entanglement generated among the photons can be swapped to the qubits, and indeed the qubits display nongaussian genuine tripartite entanglement over a w…
We propose a method to enhance bipartite and tripartite entanglement in cavity magnomechanics using an optical parametric amplifier (OPA). We analyze this system and identified parametric regimes where different types of entanglement are enhanced. We show that a proper choice of the phase of the parametric amplifier leads to the enhancement of the bipartite entanglements. Moreover, the tripartite entanglement is also significantly enhanced in the presence of OPA. The OPA not only enhances the strength of entanglement but also increases the domain of entanglement over a wider space of detunings…
The output field from a continuously driven linear parametric oscillator may exhibit considerably more squeezing than the intracavity field. Inspired by this fact, we explore the nonclassical features of the steady-state output field of a driven nonlinear Kerr parametric oscillator using a temporal wave packet mode description. Utilizing a new numerical method, we have access to the density matrix of arbitrary wave packet modes. Remarkably, we find that even though the steady-state cavity field is always characterized by a positive Wigner function, the output may exhibit Wigner negativity, dep…
Generating entangled superpositions of macroscopically distinguishable states within a parametric oscillator
我们提出了一个最近提出的实验的变体，用于产生一种新的薛定谔猫态，使用两个耦合的参数下转换器非线性晶体[F。De Martini，Phys. Rev. Lett. 81，2842（1998）]。我们研究了参量振荡器的情况，发现在适当的条件下，两个腔的反射镜沿非线性晶体的输出光束放置，可以实现薛定谔猫型纠缠态。
We study the effect of quantum entanglement maintained by virtual excitations in an ultrastrongly-coupled harmonic-oscillator system. Here, the quantum entanglement is caused by the counterrotating interaction terms and hence it is maintained by the virtual excitations. We obtain the analytical expression for the ground state of the system and analyze the relationship between the average excitation numbers and the ground-state entanglement. We also study the entanglement dynamics between the two oscillators in both the closed- and open-system cases. In the latter case, the quantum master equat…
We present squeezed light that is robust against spatial mode mismatch (beam displacement, tilt, and beam-size difference), which is generated from a self-imaging optical parametric oscillator below the threshold. We investigate the quantum properties of the generated light when the oscillator is detuned from the ideal self-imaging condition for stable operation. We find that the generated light is more robust to mode mismatch than single-mode squeezed light having the same squeezing level, and it even outperforms the single-mode infinitely squeezed light as the strength of mode mismatch incre…
