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arXiv:2008.05720 · Journal of Applied Physics

Highly nonclassical phonon emission statistics through two-phonon loss of van der Pol oscillator

Jiahua Li, Chunling Ding, Ying Wu

Published Dec 17, 2020• 8 citations
arXivHTMLPDF

Abstract

The ability to produce a nonclassical wave in a system is essential for advances in quantum communication and computation. Here, we propose a scheme to generate highly nonclassical phonon emission statistics—an antibunched wave in a quantum van der Pol (vdP) oscillator subject to external driving, both single- and two-phonon losses. It is found that phonon antibunching depends significantly on the nonlinear two-phonon loss of the vdP oscillator, where the degree of the antibunching increases monotonically with the two-phonon loss, and the distinguished parameter regimes with optimal antibunching and single-phonon emission are identified clearly. In addition, we give an in-depth insight into strong antibunching in the emitted phonon statistics by analytical calculations using a three-oscillator-level model, which agree well with the full numerical simulations employing both a master-equation approach and a Schrödinger-equation approach at weak driving. In turn, the fluorescence phonon emission spectra of the vdP oscillator, given by the power spectral density, are also evaluated. We further show that high phonon emission amplitudes, simultaneously accompanied by strong phonon antibunching, are attainable in the vdP system, which are beneficial to the correlation measurement in practical experiments. Our approach only requires a single vdP oscillator, without the need for reconfiguring the two coupled nonlinear resonators or the complex nanophononic structures as compared to the previous blockade schemes. The present scheme could inspire methods to achieve antibunching in other systems.

DOI
10.1063/5.0026286

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The ability to produce a nonclassical wave in a system is essential for advances in quantum communication and computation. Here, we propose a scheme to generate highly nonclassical phonon emission statistics—an antibunched wave in a quantum van der Pol (vdP) oscillator subject to external driving, both single- and two-phonon losses. It is found that phonon antibunching depends significantly on the nonlinear two-phonon loss of the vdP oscillator, where the degree of the antibunching increases monotonically with the two-phonon loss, and the distinguished parameter regimes with optimal antibunching and single-phonon emission are identified clearly. In addition, we give an in-depth insight into strong antibunching in the emitted phonon statistics by analytical calculations using a three-oscillator-level model, which agree well with the full numerical simulations employing both a master-equation approach and a Schrödinger-equation approach at weak driving. In turn, the fluorescence phonon emission spectra of the vdP oscillator, given by the power spectral density, are also evaluated. We further show that high phonon emission amplitudes, simultaneously accompanied by strong phonon antibunching, are attainable in the vdP system, which are beneficial to the correlation measurement in practical experiments. Our approach only requires a single vdP oscillator, without the need for reconfiguring the two coupled nonlinear resonators or the complex nanophononic structures as compared to the previous blockade schemes. The present scheme could inspire methods to achieve antibunching in other systems.
We implement nonlinear anharmonic interaction in the coupled van der Pol oscillators to investigate the quantum synchronization behavior of the systems. We study the quantum synchronization in two oscillator models, coupled quantum van der Pol oscillators and anharmonic self-oscillators. We demonstrate that the considered systems exhibit a high-order synchronization through coupling in both classical and quantum domains. We show that, due to the anharmonicity of the nonlinear interaction between the oscillators, the system exhibits phonon blockade in the phase-locking regime, which is a pure nonclassical effect and has not been observed in the classical domain. We also demonstrate that, for coupled anharmonic oscillators, the system shows a multiple resonance phase-locking behavior due to nonlinear interaction. We point out that the synchronization blockade arises due to strong anticorrelation between the oscillators, which leads to phonon antibunching in the same parametric regime. In the anharmonic oscillator case we illustrate the simultaneous occurrence of bunching and antibunching effects as a consequence of simultaneous negative and positive correlation between the anharmonic oscillators. We examine the aforementioned characteristic features in the frequency entrainment of the oscillators using a power spectrum where one can observe normal mode splitting and the Mollow triplet in the strong coupling regime. Finally, we propose a possible experimental realization for the considered system in the trapped ion and optomechanical setting.
We propose a scheme to implement the phonon antibunching and phonon blockade in a circuit quantum acoustodynamical system containing two surface acoustic wave (SAW) resonators coupled to a superconducting qubit. In the cases of driving only one SAW resonator and two SAW resonators, we investigate the phonon statistics by numerically calculating the second-order correlation function. It is found that, when only one SAW cavity is resonantly driven, the phonon antibunching effect can be achieved even when the qubit-phonon coupling strength is smaller than the decay rates of acoustic cavities. This result physically originates from the quantum interference between super-Poissonian statistics and Poissonian statistics of phonons. In particular, when the two SAW resonators are simultaneously driven under the mechanical resonant condition, the phonon antibunching effect can be significantly enhanced, which ultimately allows for the generation of a phonon blockade. Moreover, the obtained phonon blockade can be optimized by regulating the intensity ratio of the two SAW driving fields. In addition, we also discuss in detail the effect of system parameters on the phonon statistics. Our work provides an alternative way for manipulating and controlling the nonclassical effects of SAW phonons. It may inspire the engineering of new SAW-based phonon devices and extend their applications in quantum information processing.
We propose a scheme to realize antibunched multiple-photon bundles based on phonon blockade in a quadratically coupled optomechanical system. Through adjusting the detunings to match the conditions of phonon blockade in the photon sidebands, we establish super-Rabi oscillation between zero-photon state and multiple-photon states with adjustable super-Rabi frequencies under appropriate single-phonon resonant conditions. Taking the system dissipation into account, we numerically calculate the standard and generalized second-order functions of the cavity mode as well as the quantum trajectories of the state populations with Monte Carlo simulation to confirm that the emitted photons form antibunched multiple-photon bundles. Interestingly, the desirable n-photon states are reconstructed after a direct phonon emission based on phonon blockade, and thus the single-phonon emission heralds the cascade emission of n-photon bundles. Our proposal shows that the optomechanical system can simultaneously behave as antibunched multiple-photon emitter and single-phonon gun. Such a nonclassical source could have potential applications in quantum information science.
In this thesis three different approaches to control the quantum statistics in nanoscopic devices are investigated. In the first part of the thesis, mechanical oscillations in solid state devices are manipulated by an external laser to show bistabilities, coherent amplification, and enhanced damping. The dynamics is controlled by the frequency of the external laser. This study is performed in a semiclassical approximation, where expectation values of operators are factorized. These effects are used to show the similarities and differences between optomechanical systems and phonon cavities. In the regime of coherent amplification of phonons the theoretical description is extended to a fully quantum mechanical model. This reveals additional resonances due to collective processes that can be addressed via the frequency of the external laser. In the second part, a quantum light source is considered for manipulation of the emission statistics of a second quantum optical system serving as target. A Jaynes-Cummings system is used as a source that may be tuned from nonclassical to thermal emission via the pump strength. The target consists of a cavity with two emitters. The nature of the imprinted statistics is studied by higher order correlation functions. The resulting statistics deviates strongly from thermal, coherent or antibunched statistics. The third part considers coherent self feedback with time-delay, which is motivated by classical Pyragas control. The finite time delay is used as control parameter. The matrix product state evolution in the picture of the quantum stochastic Schrödinger equation is employed as a systematic way of dealing with quantum self-feedback. In this thesis, the approach is extended to include higher order terms in the time evolution operator. This is done systematically so that arbitrary order can be included enabling faster numerical evaluation. This extension of the matrix product state evolution method allows to investigate efficiently the emission statistics of a single mode cavity containing two emitters. It is shown that feedback can enhance antibunching in the light field while also counter-intuitively increasing the number of emitted photons at the same time. Expressing the time evolution operator as a sum of sparse matrices allows to include time dependent Hamiltonians in an efficient manner. Considering the pulsed excitation of a two level emitter, it is demonstrated that emission statistics may be tuned via feedback. This allows to switch between single photon emission and enhanced two photon emission.
We study quantum van der Pol oscillator in which single-photon pumping competes with a nonlinear two-photon dissipative channel to produce a quantum limit cycle, and the question of how two such oscillators with non-identical intrinsic frequencies synchronize in the sense of phase locking when coupled dissipatively to one another. For a single oscillator, starting from a Lindblad description of the dynamics, we derive the exact Wigner-function evolution equation, and show that its Fokker--Planck approximation admits in the appropriate regime an equivalent classical Itô stochastic description that reproduces remarkably well the full Lindblad dynamics. Notably, the stochastic approach provides an efficient means of capturing system dynamics in the semiclassical regime, where a large number of energy eigenstates contribute and direct numerical simulations become computationally demanding. Restricting to the three lowest Fock states and using a parity symmetry, we obtain in closed form the stationary-state density matrix and its Wigner-function representation that displays pronounced nonclassical features. For two non-identical oscillators, we study the full Lindblad dynamics numerically and characterize synchronization through the stationary-state order parameter as a function of frequency mismatch and dissipative coupling. We find that increasing the effective nonlinear dissipative strength suppresses the synchronized region. Restricting the two oscillators to the three-level qutrit subspace, a parity symmetry reduces the stationary-state problem to an exact 414141-dimensional linear system, allowing to compute the synchronization order parameter. In this reduced description, results in the limit of large dissipation agree closely with those from the full dynamics, while exhibiting in the limit of small dissipation a double-peak synchronization structure accompanied by a phase reversal.
Generating the negative Wigner functions where the corresponding Wigner states are nonclassical has been recognized as a powerful tool for successfully performing quantum information and computing protocols beyond the scope of classical computers. Here, we present the possibility to generate and engineer the negative Wigner function at a steady state using parametric (two-photon) driving and homodyne-based feedback in a quantum van der Pol (vdP) oscillator. Specifically, we employ a quantum master equation approach for calculating the Wigner function of the vdP oscillator field in phase space and, furthermore, quantifying its negativity content. We clearly show that the negative-value magnitudes, regions, and shapes of the Wigner function can be effectively tuned by the parametric driving phase and the parametric driving amplitude, as well as the feedback coefficient within a large range. We identify different contributions of these involved parameters to the Wigner-function negativity. In the present scheme, more complex quantum coherence and interference phenomena are introduced via the parametric driving and feedback, which stabilizes the phase of the vdP oscillator field and renders the capability to generate the negative Wigner function. Therefore, the enhanced Wigner-function negativity can be achieved under these optimized system parameters. Our in-depth study provides insight into the formation and in situ control of the desirable Wigner nonclassical states. The obtained results are not limited to the vdP oscillator systems and should be generally applicable to other coherent coupled systems within the reach of modern experimental facilities.