Showing papers on "Parametric oscillator published in 2019"
TL;DR: It is shown how luminal metamaterials generalize the parametric oscillator concept, realize giant broadband nonreciprocity, achieve efficient one-way amplification, pulse compression, and harmonic generation, and propose a realistic implementation in double-layer graphene.
Abstract: Time has emerged as a new degree of freedom for metamaterials, promising new pathways in wave control. However, electromagnetism suffers from limitations in the modulation speed of material parameters. Here we argue that these limitations can be circumvented by introducing a traveling-wave modulation, with the same phase velocity of the waves. We show how luminal metamaterials generalize the parametric oscillator concept, realize giant broadband nonreciprocity, achieve efficient one-way amplification, pulse compression, and harmonic generation, and propose a realistic implementation in double-layer graphene.
99 citations
TL;DR: In this article, the authors demonstrate a quantum parametric oscillator, a device with great potential in quantum error correction, and its minimal hardware design makes it a suitable building block for scalable quantum computing.
Abstract: Experiments demonstrate a quantum parametric oscillator, a device with great potential in quantum error correction. Its minimal hardware design makes it a suitable building block for scalable quantum computing.
61 citations
TL;DR: In this paper, a Traveling Wave Parametric Amplifier based on Superconducting QUantum Interference Devices (SQI) is proposed. But it is not suitable for high-frequency measurements.
Abstract: An amplifier combining noise performances as close as possible to the quantum limit with large bandwidth and high saturation power is highly desirable for many solid state quantum technologies such as high fidelity qubit readout or high sensitivity electron spin resonance for example. Here we introduce a new Traveling Wave Parametric Amplifier based on Superconducting QUantum Interference Devices. It displays a 3 GHz bandwidth, a -102 dBm 1-dB compression point and added noise near the quantum limit. Compared to previous state-of-the-art, it is an order of magnitude more compact, its characteristic impedance is in-situ tunable and its fabrication process requires only two lithography steps. The key is the engineering of a gap in the dispersion relation of the transmission line. This is obtained using a periodic modulation of the SQUID size, similarly to what is done with photonic crystals. Moreover, we provide a new theoretical treatment to describe the non-trivial interplay between non-linearity and such periodicity. Our approach provides a path to co-integration with other quantum devices such as qubits given the low footprint and easy fabrication of our amplifier.
60 citations
TL;DR: In this paper, a traveling-wave Josephson parametric amplifiers (TWJPAs) based on superconducting circuits are proposed for quantum information processing, where the interacting pump and signal/idler microwaves propagate with similar phase velocities through two different transmission lines, enabling parametric gain.
Abstract: With potentially quantum limited performance and wide frequency bandwidth, traveling-wave Josephson parametric amplifiers (TWJPAs) based on superconducting circuits are in urgent demand for quantum information processing. This study designs a TWJPA in which the interacting pump and signal/idler microwaves propagate with similar phase velocities through two different transmission lines, thereby enabling parametric gain. Such operation is possible due to a chain of SQUIDs that form the signal transmission line, which is magnetically coupled to a separate pump $L\phantom{\rule{0}{0ex}}C$ line. The proposed circuit may greatly simplify the measurement setup and solve the problem of pump depletion.
42 citations
TL;DR: In this article, a parametric resonator for vibration energy harvesting is presented, which consists of two piezoelectric cantilevers beams, each with a magnetic tip.
37 citations
TL;DR: In this paper, a half-metre wide ellipsoid filled with water is brought to solid-body rotation, and then undergoes sustained harmonic modulation of its rotation rate, triggering the exponential growth of a pair of inertial waves via a mechanism called the libration-driven elliptical instability.
Abstract: In this paper, we present an experimental investigation of the turbulent saturation of the flow driven by the parametric resonance of inertial waves in a rotating fluid. In our setup , a half-metre wide ellipsoid filled with water is brought to solid-body rotation, and then undergoes sustained harmonic modulation of its rotation rate. This triggers the exponential growth of a pair of inertial waves via a mechanism called the libration-driven elliptical instability. Once the saturation of this instability is reached, we observe a turbulent state for which energy is injected into the resonant inertial waves only. Depending on the amplitude of the rotation rate modulation, two different saturation states are observed. At large forcing amplitudes, the saturation flow mainly consists of a steady, geostrophic anticyclone. Its amplitude vanishes as the forcing amplitude is decreased while remaining above the threshold of the elliptical instability. Below this secondary transition, the saturation flow is a superposition of inertial waves which are in weakly nonlinear resonant interaction, a state that could asymptotically lead to inertial wave turbulence. In addition to being a first experimental observation of a wave-dominated saturation in unstable rotating flows, the present study is also an experimental confirmation of the model of Le Reun et al. (Phys. Rev. Lett., vol. 119 (3), 2017, 034502) who introduced the possibility of these two turbulent regimes. The transition between these two regimes and their relevance to geophysical applications are finally discussed.
33 citations
TL;DR: In this paper, the nonlinear dynamic analysis of a parametrically base excited cantilever beam based piezoelectric energy harvester is carried out, where the attached mass is placed in such a way that the system exhibits 3:1 internal resonance.
Abstract: In this work, the nonlinear dynamic analysis of a parametrically base excited cantilever beam based piezoelectric energy harvester is carried. The system consists of a cantilever beam with piezoelectric patches in bimorph configuration and attached mass at an arbitrary position. The attached mass is placed in such a way that the system exhibits 3:1 internal resonance. The governing spatio-temporal equation of motion is discretized to its temporal form by using generalized Galerkin’s method. To obtain the steady state voltage response and stability of the system, Method of multiple scales is used to reduce the resulting equation of motion into a set of first-order differential equations. The response and stability of the system under principal parametric resonance conditions has been studied. The parametric instability regions are shown for variation in different system parameters such as excitation amplitude and frequency, damping and load resistance. Bifurcations such as turning point, pitch-fork and Hopf are observed in the multi-branched non-trivial response. By tuning the attached mass an attempt has been made to harvest the electrical energy for a wider range of frequency. Such kind of smart self-sufficient systems may find application in powering low power wireless sensor nodes or micro electromechanical systems.
32 citations
TL;DR: In this article, the authors review recent advances in the research on quantum parametric phenomena in superconducting circuits with Josephson junctions and discuss physical processes in parametrically driven tunable cavity and outline theoretical foundations for their description.
Abstract: We review recent advances in the research on quantum parametric phenomena in superconducting circuits with Josephson junctions. We discuss physical processes in parametrically driven tunable cavity and outline theoretical foundations for their description. Amplification and frequency conversion are discussed in detail for degenerate and non-degenerate parametric resonance, including quantum noise squeezing and photon entanglement. Experimental advances in this area played decisive role in successful development of quantum limited parametric amplifiers for superconducting quantum information technology. We also discuss nonlinear down-conversion processes and experiments on self-sustained parametric and subharmonic oscillations.
29 citations
TL;DR: In this paper, the authors investigated the parametric resonance instability, which potentially triggers the emission of the GWs from axions, when the time evolution of the background field significantly deviates from the harmonic oscillation.
Abstract: It was recently shown that a coherent oscillation of an axion can cause an efficient parametric resonance, leading to a prominent emission of the gravitational waves (GWs). In this paper, conducting the Floquet analysis, we investigate the parametric resonance instability, which potentially triggers the emission of the GWs from axions. Such a resonance instability takes place, when the time evolution of the background field significantly deviates from the harmonic oscillation. Therefore, the resonance instability cannot be described by the Mathieu equation, whose stability/instability chart is well known. In this paper, introducing an explicitly calculable parameter , which can be used to classify different types of the parametric resonance described by the general Hill's equation, we investigate the stability/instability chart for the general Hill's equation. This can also apply to the case where the background oscillation is anharmonic. We show that the flapping resonance instability, which takes place for =O(1), typically leads to the most significant growth of the inhomogeneous modes among the self-resonance instability. We also investigate whether the flapping resonance takes place for the cosine potential or not.
29 citations
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TL;DR: In this paper, the authors review recent advances in the research on quantum parametric phenomena in superconducting circuits with Josephson junctions and discuss physical processes in parametrically driven tunable cavity and outline theoretical foundations for their description.
Abstract: We review recent advances in the research on quantum parametric phenomena in superconducting circuits with Josephson junctions. We discuss physical processes in parametrically driven tunable cavity and outline theoretical foundations for their description. Amplification and frequency conversion are discussed in detail for degenerate and non-degenerate parametric resonance, including quantum noise squeezing and photon entanglement. Experimental advances in this area played decisive role in successful development of quantum limited parametric amplifiers for superconducting quantum information technology. We also discuss nonlinear down-conversion processes and experiments on self-sustained parametric and subharmonic oscillations.
27 citations
TL;DR: In this article, the authors explored nonlinear dynamics of a supercritically moving beam under the 3:1 internal resonance condition and found that the internal resonance plays an essential role in energy transmission between related modes.
Abstract: The present work explores nonlinear dynamics of a supercritically moving beam under the 3:1 internal resonance condition. Responses are very different with those without internal resonance. Based on the direct multiple scale method, resonances for the first-two natural modes are identified to exist in three cases. The first one is that the pulsating speed frequency closes to two times of the first natural frequency. Under this condition, responses for natural modes are distinctly coupled as response curves are twisted. The internal resonance plays an essential role in energy transmission between related modes. It not only arouses a double-jumping phenomenon, but also reduces the typical parametric responses to zero astoundingly. Besides, the internal resonance changes the critical pulsating speed and produces some saddle-node bifurcations. In the case of the pulsating speed frequency closing to two times of the second natural frequency, only the second natural mode could be excited. The response occurs in the form of a typical parametric resonance. The third case is the pulsating speed frequency closing to the sum of the first-two natural frequencies. Different with the first two cases, quasi-periodic responses are found in the form of beat vibrations. Amplitude and the frequency of beats are affected by the pulsating speed, the internal resonance condition and also the pulsating frequency. Contributions of them are quite different. This paper is instructive to the study of vibration of other gyroscopic continuous systems, such as pipes conveying fluid and rotation continua.
TL;DR: In this article, the authors theoretically proposed a method for on-demand generation of traveling Schr\"odinger cat states, namely, quantum superpositions of distinct coherent states of traveling fields.
Abstract: We theoretically propose a method for on-demand generation of traveling Schr\"odinger cat states, namely, quantum superpositions of distinct coherent states of traveling fields. This method is based on deterministic generation of intracavity cat states using a Kerr-nonlinear parametric oscillator (KPO) via quantum adiabatic evolution. We show that the cat states generated inside a KPO can be released into an output mode by dynamically controlling the parametric pump amplitude. We further show that the quality of the traveling cat states can be improved by using a shortcut-to-adiabaticity technique.
TL;DR: In this article, a new type of non-degenerate parametric amplifier, which consists of a dispersion engineered Josephson junction (JJ) array, was used to detect quantum jumps of a transmon qubit with 90% fidelity.
Abstract: Determining the state of a qubit on a timescale much shorter than its relaxation time is an essential requirement for quantum information processing. With the aid of a new type of non-degenerate parametric amplifier, we demonstrate the continuous detection of quantum jumps of a transmon qubit with 90% fidelity in state discrimination. Entirely fabricated with standard two-step optical lithography techniques, this type of parametric amplifier consists of a dispersion engineered Josephson junction (JJ) array. By using long arrays, containing $10^3$ JJs, we can obtain amplification at multiple eigenmodes with frequencies below $10~\mathrm{GHz}$, which is the typical range for qubit readout. Moreover, by introducing a moderate flux tunability of each mode, employing superconducting quantum interference device (SQUID) junctions, a single amplifier device could potentially cover the entire frequency band between 1 and $10~\mathrm{GHz}$.
TL;DR: In this article, a parametrically excited magnetic rolling pendulum (MRP) with intentionally introduced nonlinearity for broadband energy harvesting was proposed, which exhibited a first-order parametric resonance with a broadened bandwidth as the excitation acceleration is ≥ 0.2
Abstract: Parametrically excited energy harvesters provide a valuable alternative to directly excited ones. However, linear energy harvesters subjected to parametric excitation usually suffer from narrow bandwidths. This letter proposes a parametrically excited magnetic rolling pendulum (MRP) with intentionally introduced nonlinearity for broadband energy harvesting. The MRP exhibited a first-order parametric resonance with a broadened bandwidth as the excitation acceleration is ≥0.2 g (g = 9.8 m/s2). When excited at 0.5 g in experiment, the parametric resonance was observed in the frequency range between 1.2 f 0 and 4.5 f 0, with f 0 being the natural frequency of 4 Hz. With a peak power output of 3.6 mW, the MRP achieved a half-power bandwidth of 4.8 Hz, which is 120% of its natural frequency. Simulation results suggest that the power output, the bandwidth, and the resonance frequency can be manipulated by varying the magnet dimensions and positions.
TL;DR: T theoretical results for the transverse motion instability of a submerged wave energy converter buoy are compared to an extensive experimental dataset, finding a good agreement with the predictions of sub-harmonic (period-doubling) sway instability using the Mathieu equation stability diagram.
Abstract: Wave energy converters and other offshore structures may exhibit instability, in which one mode of motion is excited parametrically by motion in another. Here, theoretical results for the transverse motion instability (large sway oscillations perpendicular to the incident wave direction) of a submerged wave energy converter buoy are compared to an extensive experimental dataset. The device is axi-symmetric (resembling a truncated vertical cylinder) and is taut-moored via a single tether. The system is approximately a damped elastic pendulum. Assuming linear hydrodynamics, but retaining nonlinear tether geometry, governing equations are derived in six degrees of freedom. The natural frequencies in surge/sway (the pendulum frequency), heave (the springing motion frequency) and pitch/roll are derived from the linearized equations. When terms of second order in the buoy motions are retained, the sway equation can be written as a Mathieu equation. Careful analysis of 80 regular wave tests reveals a good agreement with the predictions of sub-harmonic (period-doubling) sway instability using the Mathieu equation stability diagram. As wave energy converters operate in real seas, a large number of irregular wave runs is also analysed. The measurements broadly agree with a criterion (derived elsewhere) for determining the presence of the instability in irregular waves, which depends on the level of damping and the amount of parametric excitation at twice the natural frequency.
TL;DR: In this article, a symmetric traveling wave parametric amplifier (STWPA) based on three-wave mixing was developed and experimentally tested at 4.2 K, showing a 4 GHz bandwidth and a maximum estimated gain of 17 dB.
Abstract: We developed and experimentally tested a symmetric traveling wave parametric amplifier (STWPA) based on three-wave mixing, using the new concept of a symmetric rf-SQUID. This allowed us to fully control the second and third order nonlinearities of the STWPA by applying external currents. In this way, the optimal bias point can be reached, taking into account both phase mismatch and pump depletion minimization. The structure was tested at 4.2 K, showing a 4 GHz bandwidth and a maximum estimated gain of 17 dB.
20 Jun 2019
TL;DR: In this paper, the authors reported the detection of >70 and >45 kW radiation power at about 52μm in a 45 kW power for the far-infrared radiation.
Abstract: In the far-infrared spectrum between 20 and 60 μm, the free-electron laser (FEL) is the only wavelength-tunable coherent radiation source capable of generating kilowatt to megawatt peak powers with a linewidth of the order of 1%. Here, we report the detection of >70 kW radiation power at about 52 μm in a 45 kW radiation power for the far-infrared radiation. With 63% coupling efficiency of the silicon prism atop the KTP crystal, the measured >70 and >45 kW far-infrared radiation correspond to >111 and >71 kW powers extracted from the KTP crystal of the seeded off-axis THz parametric oscillator. The radiation source accomplished in this work has great potential to become a tabletop and economical alternative for the bulky and expensive far-infrared FELs in national facilities.
TL;DR: In this article, a quantum parametric oscillator operating at microwave frequencies was demonstrated and its dynamics and states were characterized by analyzing the output field emitted by the oscillator and implementing quantum state tomography suited for nonlinear resonators.
Abstract: Modulating the frequency of a harmonic oscillator at nearly twice its natural frequency leads to amplification and self-oscillation. Above the oscillation threshold, the field settles into a coherent oscillating state with a well-defined phase of either $0$ or $\pi$. We demonstrate a quantum parametric oscillator operating at microwave frequencies and drive it into oscillating states containing only a few photons. The small number of photons present in the system and the coherent nature of the nonlinearity prevents the environment from learning the randomly chosen phase of the oscillator. This allows the system to oscillate briefly in a quantum superposition of both phases at once - effectively generating a nonclassical Schrodinger's cat state. We characterize the dynamics and states of the system by analyzing the output field emitted by the oscillator and implementing quantum state tomography suited for nonlinear resonators. By demonstrating a quantum parametric oscillator and the requisite techniques for characterizing its quantum state, we set the groundwork for new schemes of quantum and classical information processing and extend the reach of these ubiquitous devices deep into the quantum regime.
TL;DR: A new method of measuring the continuous variable entanglement by assisting a balanced homodyne detector with the PSA and implement it experimentally finds that the normalized noise for both the difference and sum of the quadrature amplitudes of the two entangled fields fall below the shot noise limit, indicating the new method is advantageous over the traditional measurement in multi-mode case.
Abstract: Balanced homodyne detection relies on a beam splitter to superpose the weak signal input and strong local oscillator. However, recent investigation shows that a high gain phase sensitive amplifier (PSA) can be viewed as homodyne detector, in which the strong pump of PSA serves as the local oscillator [1]. Here, we analyze a new method of measuring the continuous variable entanglement by assisting a balanced homodyne detector with the PSA and implement it experimentally. Before measuring quadrature amplitude with the balanced homodyne detectors, two entangled fields generated from a pulse pumped fiber optical parametric amplifier are simultaneously coupled into the PSA. We find that the normalized noise for both the difference and sum of the quadrature amplitudes of the two entangled fields fall below the shot noise limit by about 4.6 dB, which is the record degree of entanglement measured in optical fiber systems. The experimental results illustrate that the advantages of the new measurement method include but not limit to tolerance to detection loss and characterizing entanglement with only one homodyne detector. The influence of mode-mismatching due to multi-mode property of entanglement on the measured noise reduction can also be greatly mitigated, indicating the new method is advantageous over the traditional measurement in multi-mode case.
TL;DR: The lateral nonlinear vibration of an axially moving simply supported viscoelastic nanobeam is analysed based on nonlocal strain gradient theory and shows that when subharmonic parametric resonance occurs in the system, the (non-) zero equilibrium solution and the boundary of the instability region are markedly affected by the scale parameters.
Abstract: The lateral nonlinear vibration of an axially moving simply supported viscoelastic nanobeam is analysed based on nonlocal strain gradient theory. The proposed model includes the nonlocal parameters and material characteristic length parameters, investigating the two kinds of size effects of micro-nano beam structures. Firstly, the steady-state amplitude-frequency response of the subharmonic parametric resonance is analysed by a direct multiscale method, and the stability of the (non-) zero equilibrium solution determined by the Routh-Hurwitz criterion. Subsequently, the nonlinear frequencies of the nanobeams are calculated. Finally, several numerical examples are used to illustrate the influence of the scale parameters on the nonlinear vibration characteristics of nanobeams. The results show that when subharmonic parametric resonance occurs in the system, the (non-) zero equilibrium solution and the boundary of the instability region are markedly affected by the scale parameters. In addition, the nonlocal parameters soften the system, the material characteristic length parameters harden the system, and these softening and hardening effects are strengthened (or weakened) to varying degrees in the presence of nonlinearity.
TL;DR: In this article, an oscillatory, relativistic accelerating photodetector inside a cavity is considered and the entangled photon pair production from the vacuum (Unruh effect) can be accurately described in the steady state by a nondegenerate parametric amplifier (NDPA), with the detector's accelerating center of mass serving as the parametric drive (pump).
Abstract: We consider a model for an oscillatory, relativistic accelerating photodetector inside a cavity and show that the entangled photon pair production from the vacuum (Unruh effect) can be accurately described in the steady state by a nondegenerate parametric amplifier (NDPA), with the detector's accelerating center of mass serving as the parametric drive (pump). We propose an oscillatory Unruh effect analog NDPA microwave superconducting circuit scheme, where the breathing mode of the coupling capacitance between the cavity and detector provides the mechanical pump. For realizable circuit parameters, the resulting photon production from the vacuum should be detectable.
TL;DR: In this paper, the authors investigated the influence of concentrated masses on the out-of-plane dynamic instability of a plate under the in-plane periodical loading, which has not been reported in the literature.
TL;DR: In this paper, double-clamped micro-beams are modeled as an Euler-Bernoulli beam with an axial force parameterized by the electric current, and the behavior of the beam is studied numerically and analytically, using an approximate single degree of freedom Galerkin model, reduced to the Mathieu-Duffing equation.
Abstract: We study parametric resonance (PR) of double-clamped micro-beams that are electro-thermally actuated by a time-dependent Joule’s heating and cooled by a steady air flow. The developed model demonstrates applicability of such device as a bifurcation-based flow velocity sensor. An AC electric current through the beam induces a time-harmonic compressive force that leads to parametric excitation of the structure. Convective cooling due to the air flow affects the location of the parametric transition curves on the driving voltage–frequency plane. The flow velocity can be obtained by measuring the frequency corresponding to the steep amplitude transition of the response. The device is modeled as an Euler–Bernoulli beam with an axial force parameterized by the electric current. The heat transfer problem is solved analytically; the heat flux due to the air flow is calculated using empirical correlations. The behavior of the beam is studied numerically, by means of finite differences, and analytically, using an approximate single degree of freedom Galerkin model, reduced to the Mathieu–Duffing equation. We show that while the PR always emerges at the driving voltage/current below the critical static buckling value, practical realization of the purely electro-thermal parametric excitation is challenging and is highly influenced by the device dimensions and quality factors. We evaluate the parameters required to assure the PR and demonstrate, using the model, feasibility of the suggested flow-sensing approach in the devices of realistic dimensions.
TL;DR: The Josephson Array Mode Parametric Amplifier (JAMPA) as discussed by the authors is a near-quantum-limited amplifier with a large tunable bandwidth and high dynamic range, which can be operated as a nearly quantum-limited parametric amplifier with 20 dB of gain at almost any frequency within (4-12) GHz band.
Abstract: We introduce a novel near-quantum-limited amplifier with a large tunable bandwidth and high dynamic range - the Josephson Array Mode Parametric Amplifier (JAMPA). The signal and idler modes involved in the amplification process are realized by the array modes of a chain of 1000 flux tunable, Josephson-junction-based, nonlinear elements. The frequency spacing between array modes is comparable to the flux tunability of the modes, ensuring that any desired frequency can be occupied by a resonant mode, which can further be pumped to produce high gain. We experimentally demonstrate that the device can be operated as a nearly quantum-limited parametric amplifier with 20 dB of gain at almost any frequency within (4-12) GHz band. On average, it has a 3 dB bandwidth of 11 MHz and input 1 dB compression power of -108 dBm, which can go as high as -93 dBm. We envision the application of such a device to the time- and frequency-multiplexed readout of multiple qubits, as well as to the generation of continuous-variable cluster states.
TL;DR: In this paper, the performance of a bimorph cantilever energy harvester subjected to horizontal and vertical excitations is investigated and the results reveal that the bending deformation generated by direct excitation pushes the system out of axial deformation and overcomes the limitation of initial threshold of parametric excitation system.
Abstract: The performance of bimorph cantilever energy harvester subjected to horizontal and vertical excitations is investigated. The energy harvester is simulated as an inextensible piezoelectric beam with the Euler–Bernoulli assumptions. A horizontal base excitation along the axis of the beam is converted into the parametric excitation. The governing equations include geometric, inertia and electromechanical coupling nonlinearities. Using the Galerkin method, the electromechanical coupling Mathieu–Duffing equation is developed. Analytical solutions of the frequency response curves are presented by using the method of multiple scales. Some analytical results are obtained, which reveal the influence of different parameters such as the damping, load resistance and excitation amplitude on the output power of the energy harvester. In the case of parametric excitation, the effect of mechanical damping and load resistance on the initiation excitation threshold is studied. In the case of combination of parametric and direct excitations, the dynamic characteristics and performance of the nonlinear piezoelectric energy harvesters are studied. Our studies revealed that the bending deformation generated by direct excitation pushes the system out of axial deformation and overcomes the limitation of initial threshold of parametric excitation system. The combination of parametric and direct excitations, which compensates and complements each other, can be served as a better solution which enhances performance of energy harvesters.
TL;DR: In this article, the authors studied the entanglement evolution in the dynamical Casimir effect by computing the time-dependent R\'enyi and von Neumann entropy analytically in arbitrary dimensions.
Abstract: The particles produced from the vacuum in the dynamical Casimir effect are highly entangled. In order to quantify the correlations generated by the process of vacuum decay induced by moving mirrors, we study the entanglement evolution in the dynamical Casimir effect by computing the time-dependent R\'enyi and von Neumann entanglement entropy analytically in arbitrary dimensions. We consider the system at parametric resonance, where the effect is enhanced. We find that, in ($1+1$) dimensions, the entropies grow logarithmically for large times, ${S}_{A}(\ensuremath{\tau})\ensuremath{\sim}\frac{1}{2}\mathrm{log}(\ensuremath{\tau})$, while in higher dimensions ($n+1$) the growth is linear, ${S}_{A}(t)\ensuremath{\sim}\ensuremath{\lambda}\ensuremath{\tau}$, where $\ensuremath{\lambda}$ can be identified with the Lyapunov exponent of a classical instability in the system. In ($1+1$) dimensions, strong interactions among field modes prevent the parametric resonance from manifesting as a Lyapunov instability, leading to a sublinear entropy growth associated with a constant rate of particle production in the resonant mode. Interestingly, the logarithmic growth comes with a prefactor of $1/2$ which cannot occur in time-periodic systems with finitely many degrees of freedom and is thus a special property of bosonic field theories.
TL;DR: In this article, a near-quantum-limited parametric amplifier based on the nonlinear dynamics of quasiparticles flowing through a superconducting-insulator-superconducting junction was proposed.
Abstract: We theoretically investigate a near-quantum-limited parametric amplifier based on the nonlinear dynamics of quasiparticles flowing through a superconducting-insulator-superconducting junction. Photon-assisted tunneling, resulting from the combination of dc- and ac-voltage bias, gives rise to a strong parametric interaction for the electromagnetic modes reflected by the junction coupled to a transmission line. We show phase-sensitive and phase-preserving amplification, together with single- and two-mode squeezing. For an aluminum junction pumped at twice the center frequency, $\omega_0/2\pi=6$~GHz, we predict narrow-band phase-sensitive amplification of microwaves signals to more than 20 dB, and broadband phase-preserving amplification of 20 dB over a 1.2 GHz 3-dB bandwidth. We also predict single- and two-mode squeezing reaching more than -12 dB over 5.3 GHz 3-dB bandwidth. Moreover, with a simple impedance matching circuit, we demonstrate 3 dB bandwidth reaching 4.3 GHz for 20 dB of gain. A key feature of the device is that its performance can be controlled in-situ with the applied dc- and ac-voltage biases.
TL;DR: In this paper, the authors used a compact crystalline whispering gallery mode resonator made of lithium niobate as a degenerate parametric oscillator for nonclassical light.
Abstract: Squeezed vacuum states enable optical measurements below the quantum limit and hence are a valuable resource for applications in quantum metrology and also quantum communication. However, most available sources require high pump powers in the milliwatt range and large setups, which hinders real world applications. Furthermore, degenerate operation of such systems presents a challenge. Here, we use a compact crystalline whispering gallery mode resonator made of lithium niobate as a degenerate parametric oscillator. We demonstrate about 1.4 dB noise reduction below the shot noise level for only 300 $\mu\text{W}$ of pump power in degenerate single mode operation. Furthermore, we report a record pump threshold as low as 1.35 $\mu\text{W}$. Our results show that the whispering gallery based approach presents a promising platform for a compact and efficient source for nonclassical light.
TL;DR: In this paper, a parametric modulation of the nanobeam resonance frequency can realize a phase-sensitive parametric amplifier for intracavity microwave photons, which allows for simultaneous cooling of the mechanical element, which potentially enables this type of optomechanical microwave amplifier to be quantum-limited.
Abstract: Microwave optomechanical circuits have been demonstrated in the past years to be extremely powerfool tools for both, exploring fundamental physics of macroscopic mechanical oscillators as well as being promising candidates for novel on-chip quantum limited microwave devices. In most experiments so far, the mechanical oscillator is either used as a passive device element and its displacement is detected using the superconducting cavity or manipulated by intracavity fields. Here, we explore the possibility to directly and parametrically manipulate the mechanical nanobeam resonator of a cavity electromechanical system, which provides additional functionality to the toolbox of microwave optomechanical devices. In addition to using the cavity as an interferometer to detect parametrically modulated mechanical displacement and squeezed thermomechanical motion, we demonstrate that parametric modulation of the nanobeam resonance frequency can realize a phase-sensitive parametric amplifier for intracavity microwave photons. In contrast to many other microwave amplification schemes using electromechanical circuits, the presented technique allows for simultaneous cooling of the mechanical element, which potentially enables this type of optomechanical microwave amplifier to be quantum-limited.
TL;DR: In this article, a time lens is used to resolve the temporal dynamics over successive round-trips, allowing crystal clear evidence of the existence of P1-P2 transitions for suitable changes of cavity parameters, as well as for the successful characterization of the relative temporal patterns.
Abstract: Modulational instability in passive optical resonators, the triggering mechanism of frequency comb and pulse train generation, is shown to exhibit transitions between regimes involving period-one (P1) versus period-two (P2) dynamical evolutions. The latter is a signature of parametric resonance occurring in the system, which can arise either from intrinsic cavity periodicity or from spatial modulation of the cavity parameters. We characterize the P1-P2 transition for both cases employing a fiber resonator where the intra-cavity fiber can be either uniform or dispersion modulated. The key element of our setup is a time lens which we exploit to resolve the temporal dynamics over successive round-trips, allowing crystal clear evidence of the existence of P1-P2 transitions for suitable changes of cavity parameters, as well as for the successful characterization of the relative temporal patterns. Our findings reveal new regimes where the averaged model known as Lugiato-Lefever equation turns out to be inadequate to explain the dynamics, whereas the results are correctly predicted and described on the basis of the full Ikeda map.