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arXiv:2306.11350 · Physical Review A

Nonclassical radiation from a nonlinear oscillator driven solely by classical 1/f noise

Archak Purkayastha, Klaus Mølmer

Published Nov 7, 2023• 1 citation
arXivHTMLPDF

Abstract

Low-frequency classical $1/f$ noise and quantum noise from low-temperature phonon modes are ubiquitous across various experimental platforms, and are usually considered a hindrance for quantum technological applications. Here we show that the simultaneous action of classical $1/f$ noise and a low-temperature phonon bath on a nonlinear oscillator can result in the generation of nonclassical antibunched radiation without the need for any additional drive. The $1/f$ noise itself provides the source of energy for generation of photons, while the phonon bath prevents heating up to infinite temperature and takes the nonlinear oscillator to a noise-averaged nonequilibrium steady state. The photon current in this nonequilibrium steady state may be detected by a standard wide-band detector. For sufficient nonlinearity and frequency dependence of the effective noise spectrum, the detected radiation can be antibunched. This opens the possibility to turn two of the most ubiquitous intrinsic noises in experimental platforms from a hindrance to a resource. It shows that wasteful heat from unavoidable noises can be converted into useful radiation. These results are based on the Redfield equation, which provides a rigorously derived general approach to treat any type of weak noise in a quantum system, specified only via the noise spectral function, as we discuss in detail.

DOI
10.1103/physreva.108.053704

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Low-frequency classical 1/f1/f1/f noise and quantum noise from low-temperature phonon modes are ubiquitous across various experimental platforms, and are usually considered a hindrance for quantum technological applications. Here we show that the simultaneous action of classical 1/f1/f1/f noise and a low-temperature phonon bath on a nonlinear oscillator can result in the generation of nonclassical antibunched radiation without the need for any additional drive. The 1/f1/f1/f noise itself provides the source of energy for generation of photons, while the phonon bath prevents heating up to infinite temperature and takes the nonlinear oscillator to a noise-averaged nonequilibrium steady state. The photon current in this nonequilibrium steady state may be detected by a standard wide-band detector. For sufficient nonlinearity and frequency dependence of the effective noise spectrum, the detected radiation can be antibunched. This opens the possibility to turn two of the most ubiquitous intrinsic noises in experimental platforms from a hindrance to a resource. It shows that wasteful heat from unavoidable noises can be converted into useful radiation. These results are based on the Redfield equation, which provides a rigorously derived general approach to treat any type of weak noise in a quantum system, specified only via the noise spectral function, as we discuss in detail.
We investigate statistics of the photon (phonon) field undergoing linear and nonlinear damping processes. An effective two-photon (phonon) nonlinear ``cooling by heating'' process is realized from linear damping by spectral filtering of the heat baths present in the system. This cooling process driven by incoherent quantum thermal noise can create quantum states of the photon field. In fact, for high temperatures of the spectrally filtered heat baths, sub-Poissonian statistics with strong antibunching in the photon (phonon) field are reported. This notion of the emergence and control of quantumness by incoherent thermal quantum noise is applied to a quantum system comprised of a two-level system and a harmonic oscillator or analogous optomechanical setting. Our analysis may provide a promising direction for the preparation and protection of quantum features via nonlinear damping that can be controlled with incoherent thermal quantum noise.
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.
Coherent states and their generalizations are normally appropriate candidates for describing radiation fields. Despite this, the effect of thermal noise on generalized coherent states has not been extensively studied. In fact, thermal effects are unavoidable at finite temperatures, and they should be taken into account to have a better agreement with experimental results. In this regard, we use the concept of thermal coherent states, which are indeed the standard coherent states including thermal effects. So, in this paper, by using a nonlinear coherent states approach, we generalize the thermal coherent states to their nonlinear counterparts. In other words, we find a natural link between the thermal coherent states and the nonlinear coherent states associated with nonlinear oscillator algebra. Afterwards, the nonclassicality features of the obtained states are numerically investigated to explore the roles of both nonlinearity and thermal noise in physical properties. The results show that the thermal effects lead to the transition from nonclassical states to classical ones. Moreover, it is seen that the operator-valued intensity-dependent function plays a leading role in controlling the depth as well as the domain of nonclassicality aspects.
In recent years, significant progress has been made to push micro-, nano-, and optomechanical systems into the quantum regime. The common goal is to demonstrate and control quantum effects in these systems, which enable applications in quantum metrology and quantum information processing. This process is hampered by dissipation, i.e., the interaction of these systems with their environment. \n \n \nIn this thesis, we focus on two different aspects of dissipative nonlinear systems in the quantum regime. In the first part, we study how states with genuinely quantum properties can be generated by a continuous measurement of the interaction between the quantum system and its environment. This approach turns dissipation into a useful tool to generate nonclassical states of light and matter, which have been identified as important resources for quantum-enhanced sensing, quantum communication, and quantum error processing. We discuss the generation of mechanical states with a sub-Poissonian phonon-number distribution in an optomechanical phonon laser beyond the resolved-sideband regime, and we propose a heralded protocol to generate nonclassical states by photon-counting measurements. We apply this protocol to a Kerr nonlinear oscillator and show that it enables the creation of states with a negative Wigner function although the steady-state Wigner function of this system is strictly positive. \n \n \nIn the second part of this thesis, we focus on self-sustained oscillators in the quantum regime. If a weak perturbation is applied to a self-sustained oscillator, the oscillator can adjust its frequency of oscillation. This effect is called synchronization and has been identified as a universal feature of many different complex classical systems, e.g., electrical circuits, biological systems, and power grids. In recent years, several theoretical proposals have been put forward to study synchronization in the quantum regime. However, an experimental demonstration of quantum effects in synchronization has still been missing. \n \n \nWe develop an analytical framework to study the synchronization of a quantum self-sustained oscillator to an external signal. This framework establishes a unified description of the above-mentioned proposals and allows us to identify the quantum-mechanical resource of synchronization. Based on these findings, we discover a novel interference-based quantum synchronization blockade effect and we derive a bound on the maximum degree of synchronization that can be achieved in the quantum regime. The framework also reveals a large freedom in tailoring a quantum system that is able to synchronize. Taking advantage of this freedom, we propose alternative implementations of quantum self-sustained oscillators that reduce the experimental challenges. \n \n \nFinally, we use digital quantum simulation to implement a quantum self-sustained oscillator on a current quantum computer. Applying an external signal to the oscillator, we verify typical features of quantum synchronization, and we demonstrate interference-based quantum synchronization blockade. Our results are the first experimental demonstration of genuinely quantum effects in synchronization and they show that state-of-the-art noisy intermediate-scale quantum computers are powerful enough to implement and study realistic dissipative quantum systems. \n
We introduce a functional perturbative method for treating weakly nonlinear systems coupled with a quantum field bath. We demonstrate using this method to obtain the covariance matrix elements and the correlation functions of a quantum anharmonic oscillator interacting with a heat bath. We identify a fluctuation-dissipation relation based on the nonequilibrium dynamics of this nonlinear open quantum system. To establish its connection with dynamical equilibration, we further examine the energy flows between the anharmonic oscillator and the bath field. The vanishing of the net flow is an indication of the existence of an equilibrium state for such an open-system configuration. The results presented here are useful for studying the nonequilibrium physical processes of nonlinear quantum systems such as heat transfer or electron transport.
Understanding nonequilibrium transport and fluctuations driven by nonclassical light in nonlinear quantum optical systems is challenging. Here, we formulate a driven quantum master equation in the rotating frame combined with full counting statistics, retaining the drive-induced frequency shifts in the system-reservoir interactions and providing a unified description of drive-assisted incoherent transitions based on the rotated system dressed-basis. Applied to a Kerr resonator and a nonlinear Jaynes-Cummings model, the approach reveals pronounced multiphoton-resonant enhancement of the drive input energy current, with significant high peaks under two-photon driving compared to the single-photon case. The two-photon resonance relations are analytically obtained. Resonance structure in the nonlinear Jaynes-Cummings model nonlinearly relies on qubit-photon couplings, with additional dressed-state branches. A low-energy-state approximation attributes the resonant current enhancement to dressed-state hybridization and efficient activation of incoherent energy exchange processes. Beyond the average current, two-photon-driving induced energy exchange picture near resonance also substantially modifies the second-order current fluctuation and higher-order current cumulant, while increasing the time-normalized signal-to-noise ratio. Adding two-photon loss introduces extra incoherent photon-pair exchange pathways and further reshapes the current and its fluctuations. We hope these results may deepen interpretation of photon driving and quantum dissipation cooperatively governing nonequilibrium energy transport and fluctuations.