Lorenza Viola, Roberto Onofrio, Tommaso Calarco
The measurement process is introduced in the dynamics of Josephson devices exhibiting quantum behaviour in a macroscopic degree of freedom. The measurement is shown to give rise to a dynamical damping mechanism whose experimental observability could be relevant to understand decoherence in macroscopic quantum systems.
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We give a simple way to detect the geometric phase shift and the conditional geometric phase shift with Josephson junction system. Comparing with the previous work(Falcl G, Fazio R, Palma G.M., Siewert J and Verdal V, {\it Nature} {\bf 407}, 355(2000)), our scheme has two advantages. We use the non-adiabatic operation, thus the detection is less affected by the decoherence. Also, we take the time evolution on zero dynamic phase loop, we need not take any extra operation to cancel the dynamic phase.
We suggest a procedure for demonstrating quantum coherence and measuring decoherence times between different fluxoid states of a SQUID by using ``adiabatic inversion'', where one macroscopic fluxoid state is smoothly transferred into the other, like a spin reversing direction by following a slowly moving magnetic field. This is accomplished by sweeping an external applied flux, and depends on a well-defined quantum phase between the two macroscopic states. Varying the speed of the sweep relative to the decoherence time permits one to move from the quantum regime, where such a well-defined phas…
In this paper we explore the quantum behaviour of a SQUID ring which has a significant Josephson coupling energy. We show that that the eigenfunctions of the Hamiltonian for the ring can be used to create macroscopic quantum superposition states of the ring. We also show that the ring potential may be utilised to squeeze coherent states. With the SQUID ring as a strong contender as a device for manipulating quantum information, such properties may be of great utility in the future. However, as with all candidate systems for quantum technologies, decoherence is a fundamental problem. In this pa…
A procedure for demonstrating quantum coherence and measuring decoherence times between different fluxoid states of a SQUID by using ``adiabatic inversion'' is discussed. One fluxoid state is smoothly transferred into the other, like a spin reversing direction by following a slowly moving magnetic field. This is accomplished by sweeping an external applied flux, and depends on a well-defined quantum phase between the two macroscopic states. Varying the speed of the sweep relative to the decoherence time permits one to move from the quantum regime, where such a well-defined phase exists, to the…
Temporal Bell-like inequalities are derived taking into account the influence of the measurement apparatus on the observed magnetic flux in a rf-SQUID. Quantum measurement theory is shown to predict violations of these inequalities only when the flux states corresponding to opposite current senses are not distinguishable. Thus rf-SQUIDs cannot help to discriminate realism and quantum mechanics at the macroscopic level.
We show how macroscopically distinct quantum superposition states (Schroedinger cat states) may be used as logical qubit encodings for the correction of spontaneous emission errors. Spontaneous emission causes a bit flip error which is easily corrected by a standard error correction circuit. The method works arbitrarily well as the distance between the amplitudes of the superposed coherent states increases.
We introduce a technique to control the macroscopic quantum state of an rf SQUID qubit. We propose to employ a stream of single flux quantum (SFQ) pulses magnetically coupled to the qubit junction to momentarily suppresses its critical current. This effectively lowers the barrier in the double-well rf-SQUID potential thereby increasing the tunneling oscillation frequency between the wells. By carefully choosing the time interval between SFQ pulses one may accelerate the interwell tunneling rate. Thus it is possible to place the qubit into a chosen superposition of flux states and then effectiv…
We study a system of two nanomechanical resonators embedded in a dc SQUID. We show that the inductively-coupled resonators can be treated as two entangled quantum memory elements with states that can be read from, or written on by employing the SQUID as a displacement detector or switching additional external magnetic fields, respectively. We present a scheme to squeeze the even modeof the state of the resonators and consequently reduce the noise in the measurement of the magnetic flux threading the SQUID. Wefinally analyze the effect of dissipation on the squeezing using the quantum master eq…
We report a detailed theoretical study of a coherent macroscopic quantum-mechanical phenomenon - quantum beats of a single magnetic fluxon trapped in a two-cell SQUID of high kinetic inductance. We calculate numerically and analytically the low-lying energy levels of the fluxon, and explore their dependence on externally applied magnetic fields. The quantum dynamics of the fluxon shows quantum beats originating from its coherent quantum tunneling between the SQUID cells. We analyze the experimental setup based on a three-cell SQUID, allowing for time-resolved measurements of quantum beats of t…
We believe that the best chance to observe macroscopic quantum coherence (MQC) in a rf-SQUID qubit is to use on-chip RSFQ digital circuits for preparing, evolving and reading out the qubit's quantum state. This approach allows experiments to be conducted on a very short time scale (sub-nanosecond) without the use of large bandwidth control lines that would couple environmental degrees of freedom to the qubit thus contributing to its decoherence. In this paper we present our design of a RSFQ digital control circuit for demonstrating MQC in a rf-SQUID. We assess some of the key practical issues …
We irradiated an rf-SQUID qubit with large-amplitude and high frequency electromagnetic field. Population transitions between macroscopic distinctive quantum states due to Landau-Zener transitions at energy-level avoided crossings were observed. The qubit population on the excited states as a function of flux detuning and microwave power exhibits interference patterns. Some novel features are found in the interference and a model based on rate equations can well address the features.
We consider the interaction of a quantum mechanical SQUID ring with a classical resonator (a parallel $LC$ tank circuit). In our model we assume that the evolution of the ring maintains its quantum mechanical nature, even though the circuit to which it is coupled is treated classically. We show that when the SQUID ring is driven by a classical monochromatic microwave source, energy can be transferred between this input and the tank circuit, even when the frequency ratio between them is very large. Essentially, these calculations deal with the coupling between a single macroscopic quantum objec…
Microwave resonances between discrete macroscopically distinct quantum states with single photon and multiphoton absorption are observed in a strongly driven radio frequency superconducting quantum interference device flux qubit. The amplitude of the resonant peaks and dips are modulated by the power of the applied microwave irradiation and a population inversion is generated at low flux bias. These results, which can be addressed with Landau-Zener transition, are useful to develop an alternative means to initialize and manipulate the flux qubit, as well as to do a controllable population inve…
Quantum phenomena appear in a macroscopic scale in Bose-Einstein condensates. The Gross-Pitaevskii (GP) equation describes the dynamics of the weakly interacting Bose-Einstein condensates. The GP equation has a form of the Schroedinger equation with self-interaction. The coupled Gross-Pitaevskii equations are used to describe some mixtures of Bose-Einstein condensates. In this paper, we will show some numerical results of coupled Gross-Pitaevskii equations without self-interaction, which has a form of nonlinearly-coupled Schroedinger equations. We demonstrate that the macroscopic oscillation a…
Nanohertz Pendulum toward Macroscopic Entanglement under Structural Damping
该研究针对结构阻尼产生的1/f力噪声谱损害宏观纠缠的问题，研制出7毫克的阶梯式熔融石英纤维悬挂摆，测得增益超出所需要求，为宏观纠缠实现提供了可行方案。
We present a new theoretical approach to describe the quantum behavior of a macroscopic system interacting with an external irradiation field, close to the resonant condition. Here we consider the extremely underdamped regime for a system described by a double well potential. The theory includes both: transitions from one well to the other and relaxation processes. We simulate resonant phenomena in a rf-SQUID, whose parameters lie in the range typically used in the experiments. The dependence of the transition probability W on the external drive of the system $ϕ_x$ shows three resonance peaks.…
Macroscopic quantum tunneling of the phase is a fundamental phenomenon in the quantum dynamics of superconducting nanocircuits. The tunneling rate can be controlled in such circuits, where the potential landscape for the phase can be tuned with different external bias parameters. Precise theoretical knowledge of the macroscopic quantum tunneling rate is required in order to simulate and understand the experiments. We present a derivation, based on the instanton technique, of an analytical expression of the escape rate in general quartic and symmetric sextic potentials comprising two escape pat…
We study a device consisting of a dc-SQUID with two sections of its loop acting as two mechanical resonators. An analog of the parametric down-conversion process in quantum optics can be realized with this device. We show that a two-mode squeezed state can be generated for two overdamped mechanical resonators, where the damping constants of the two mechanical resonators are larger than the coupling strengths between the dc-SQUID and the two mechanical resonators. Thus we show that entangled states of these two mechanical resonators can be generated.
The physics of quantum electromagnetism in an absorbing medium is that of a field of damped harmonic oscillators. Yet until recently the damped harmonic oscillator was not treated with the same kind of formalism used to describe quantum electrodynamics in a arbitrary medium. Here we use the techniques of macroscopic QED, based on the Huttner--Barnett reservoir, to describe the quantum mechanics of a damped oscillator. We calculate the thermal and zero-point energy of the oscillator for a range of damping values from zero to infinity. While both the thermal and zero-point energies decrease with…
A magnetically levitated conducting rotor with ultra-low rotational damping circumventing eddy loss
本文提出并验证了一种在高真空中轴对称磁场内抗磁性悬浮的导电转子，通过解析证明与实验模拟表明其可规避涡流阻尼，实现极低旋转阻尼，为超低损耗转子在陀螺仪、压力传感及基础物理测试中的应用奠定基础。
We suggest a system in which the amplitude of macroscopic flux tunneling can be modulated via the Aharonov-Casher effect. The system is an rf-SQUID with the Josephson junction replaced by a Bloch transistor -- two junctions separated by a small superconducting island on which the charge can be induced by an external gate voltage. When the Josephson coupling energies of the junctions are equal and the induced charge is q=e, destructive interference between tunneling paths brings the flux tunneling rate to zero. The device may also be useful as a qubit for quantum computation.
The recovery of classical chaotic dynamics from quantum systems has long been a subject of interest. Furthermore, recent work indicates that quantum chaos may well be significant in quantum information processing. In this paper we discuss the quantum to classical crossover of a superconducting quantum inference device (SQUID) ring. Such devices comprise of thick superconducting loop enclosing a Josephson weak link. These devices are currently strong candidates for many applications in quantum technologies. The weak link brings with it a non-linearity such that semi-classical models of this sys…
We propose an effective realization of the universal set of elementary quantum gates in solid state quantum computer based on macroscopic (or mesoscopic) resonance systems - multi-atomic coherent ensembles, squids or quantum dots in quantum electrodynamic cavity. We exploit an encoding of logical qubits by the pairs of the macroscopic two- or three-level atoms that is working in a Hilbert subspace of all states inherent to these atomic systems. In this subspace, logical single qubit gates are realized by the controlled reversible transfer of single atomic excitation in the pair via the exchang…
We propose a scheme to prepare macroscopic quantum superpositions of motion in optomachanical nano- or micromechanical oscillators quadratically coupled to an intracavity field. The nonlinear optomechanical coupling leads to an effective degenerate three-wave mixing interaction between the mechanical and cavity modes. The quantum superpositions result from the combined effects of the interaction and cavity dissipation. We show analytically and confirm numerically that various deterministic quantum superpositions can be achieved, depending on initial mechanical state. The effect of mechanical d…
We formulate a model for the steady state response of a nonlinear quantum oscillator structure, such as those used in a variety of superconducting qubit experiments, when excited by a steady, but not necessarily small, ac tone. We show that this model can be derived directly from a circuit description of some recent qubit experiments in which the state of the qubit is read out directly, without a SQUID magnetometer. The excitation profile has a rich structure depending on the detuning of the tone from the small-signal resonant frequency, on the degree of damping, and on the excitation amplitud…
We present a microwave quantum refrigeration principle based on the Josephson effect. When a superconducting quantum interference device (SQUID) is pierced by a time-dependent magnetic flux, it induces changes in the macroscopic quantum phase and an effective finite bias voltage appears across the SQUID. This voltage can be used to actively cool well below the lattice temperature one of the superconducting electrodes forming the interferometer. The achievable cooling performance combined with the simplicity and scalability intrinsic to the structure pave the way to a number of applications in …
The Caldeira-Leggett Hamiltonian (Eq. (1) below) describes the interaction of a discrete harmonic oscillator with a continuous bath of harmonic oscillators. This system is a standard model of dissipation in macroscopic low temperature physics, and has applications to superconductors, quantum computing, and macroscopic quantum tunneling. The similarities between the Caldeira-Leggett model and the linearized Vlasov-Poisson equation are analyzed, and it is shown that the damping in the Caldeira-Leggett model is analogous to that of Landau damping in plasmas [1]. An invertible linear transformatio…
We identify a class of quantum states, each consisting of a microscopic and a macroscopic section, that are effectively decoherence-free when each particle is locally passed through a quantum channel. In particular, and in contrast to other macroscopic quantum states like the Greenberger-Horne-Zeilinger state, the content of entanglement and other quantum correlations in the microscopic to macroscopic partition of this class of states is independent of the number of particles in their macroscopic sectors, when all the particles suffer passage through local amplitude and phase damping channels.…
We report on measurements of flux and charge noise in an rf-SQUID flux qubit using macroscopic resonant tunneling (MRT). We measure rates of incoherent tunneling from the lowest energy state in the initial well to the ground and first excited states in the target well. The result of the measurement consists of two peaks. The first peak corresponds to tunneling to the ground state of the target well, and is dominated by flux noise. The second peak is due to tunneling to the excited state and is wider due to an intrawell relaxation process dominated by charge noise. We develop a theoretical mode…
Time-dependent linear coupling between macroscopic quantum resonator modes generates both a parametric amplification also known as a {}"squeezing operation" and a beam splitter operation, analogous to quantum optical systems. These operations, when applied properly, can robustly generate entanglement and squeezing for the quantum resonator modes. Here, we present such coupling schemes between a nanomechanical resonator and a superconducting electrical resonator using applied microwave voltages as well as between two superconducting lumped-element electrical resonators using a r.f. SQUID-mediat…
A hybrid quantum system is proposed by coupling the internal hyperfine transitions of a trapped atomic Bose-Einstein condensate (BEC) and a superconducting quantum interference device (SQUID) via the macroscopic quantum field of the flux qubit. The presence of the condensate leads to a bosonic enhancement of the Rabi frequency over the otherwise small single-particle magnetic dipole transition matrix elements. This enhancement allows for the possibility to rapidly transfer and store qubit states in the BEC that were originally prepared in the SQUID. The fidelity of this transfer for different …
A recent Letter [1] has proposed a device, consisting of an rf SQUID with the junction replaced by a double one, i.e. a Bloch transistor. For symmetric Josephson couplings, and for specific flux bias and gate voltage applied to the transistor's island, the tunneling of encircled flux between its two local potential minima is claimed to be suppressed completely due to destructive interference. This comment purports to show that this claim in general is not valid. Namely, the very Hamiltonian (1) in [1], from which the effect is derived, describes the circuit only under an additional condition. …
We propose to couple a trapped single electron to superconducting structures located at a variable distance from the electron. The electron is captured in a cryogenic Penning trap using electric fields and a static magnetic field in the Tesla range. Measurements on the electron will allow investigating the properties of the superconductor such as vortex structure, damping and decoherence. We propose to couple a superconducting microwave resonator to the electron in order to realize a circuit QED-like experiment, as well as to couple superconducting Josephson junctions or superconducting quantu…
By means of a two-mode model, we show that transitions to different arrays of coexistent regimes in the phase space can be attained by rotating a double-well system, which consists of a toroidal condensate with two diametrically placed barriers. Such a configuration corresponds to the atomtronic counterpart of the well-known direct-current superconducting quantum interference device. Due to the phase gradient experimented by the on-site localized functions when the system is subject to rotation, a phase difference appears on each junction in order to satisfy the quantization of the velocity fi…
The quantum states of flux qubit is suggested to observe with the help of a new device, the superconducting differential double contour interferometer (DDCI). The flux qubit and the superconducting quantum interference device (DC-SQUID) are connected in the DDCI through the phase of the wave function rather than through magnetic flux. The critical current of DC-SQUID should change to the maximum value at the change of the flux qubit state thanks to this phase coupling. A large jump in the critical current and voltage enables to observe continuously the change in time the state of the flux qubi…
Levitated nanoparticles and microparticles are excellent candidates for the realization of extremely isolated mechanical systems, with a huge potential impact in sensing applications and in quantum physics. Magnetic levitation based on static fields is a particularly interesting approach, due to the unique property of being completely passive and compatible with low temperatures. Here, we show experimentally that micromagnets levitated above type-I superconductors feature very low damping at low frequency and low temperature. In our experiment, we detect 5 out of 6 rigid-body mechanical modes …
Spontaneous Macroscopic Quantum Synchronization in an Ensemble of Two-level Systems
本文研究了两能级系统集合中自发生宏观量子同步现象，通过建立非线性量子主方程，分析了相互作用和耗散对系统同步状态的影响，并绘制了同步相图，展示了不同自然频率组之间的完全同步和部分同步。
We present a scheme to deterministically prepare non-classical quantum states of a massive mirror including highly non-Gaussian states exhibiting sizeable negativity of the Wigner function. This is achieved by exploiting the non-linear light-matter interaction in an optomechanical cavity by driving the system with optimally designed frequency patterns. Our scheme reveals to be resilient against mechanical and optical damping, as well as mechanical thermal noise and imperfections in the driving scheme. Our proposal thus opens a promising route for table-top experiments to explore and exploit ma…
Apparent nonlinear damping triggered by quantum fluctuations
研究超导谐振器中非线性阻尼的起源，发现量子涨落与约瑟夫森结非线性的相互作用会产生类似非线性阻尼的功率依赖性，该表观效应也适用于纳米机械振荡器等具有保守非线性的系统。
Macroscopic fields like electromagnetic, MHD, acoustic or gravitational waves are usually described by classical wave equations with possible additional damping terms and coherent sources. The aim of this paper is to develop a complete macroscopic formalism including random/thermal sources, dissipation and random scattering of waves by environment. The proposed reduced state of field (RSF) combines averaged field with the two-point correlation function called single-particle density matrix. The evolution equations for RSF is obtained by reduction of the generalized quasi-free dynamical semigro…
Quadrature squeezing enhances Wigner negativity in a mechanical Duffing oscillator
提出利用运动压缩态有效增强量子非谐谐振子的非谐性，加速 Wigner 分布负性产生并抑制能量阻尼，为宏观机械系统制备真正量子态提供了理论与实验平台分析。
Unbiased Estimation of Conditional Covariance for Quantum Optomechanics
研究量子光力学中条件协方差的无偏估计问题，通过从因果、追溯和平滑轨迹推导线性高斯估计器，解决传统方法有偏差的问题，为无偏测试宏观纠缠铺平道路，适用于多种规模的测试质量。
Energy-efficient classical information processing and storage based on topological defects in magnetic systems have been studied over past decade. In this work, we introduce a class of macroscopic quantum devices in which a quantum state is stored in a topological defect of a magnetic insulator. We propose non-invasive methods to coherently control and readout the quantum state using ac magnetic fields and magnetic force microscopy, respectively. This macroscopic quantum spintronic device realizes the magnetic analog of the three-level rf-SQUID qubit and is built fully out of electrical insula…
We analyze a quantum-classical hybrid system of steadily precessing slow classical localized magnetic moments, forming a head-to-head domain wall, embedded into an open quantum system of fast nonequilibrium electrons. The electrons reside within a metallic wire connected to macroscopic reservoirs. The model captures the essence of dynamical noncollinear and noncoplanar magnetic textures in spintronics, while making it possible to obtain the exact time-dependent nonequilibrium density matrix of electronic system and split it into four contributions. The Fermi surface contribution generates diss…
The Josephson effect represents perhaps the prototype of macroscopic phase coherence and is at the basis of the most widespread interferometer, i.e., the superconducting quantum interference device (SQUID). Yet, in analogy to electric interference, Maki and Griffin predicted in 1965 that thermal current flowing through a temperature-biased Josephson tunnel junction is a stationary periodic function of the quantum phase difference between the superconductors. The interplay between quasiparticles and Cooper pairs condensate is at the origin of such phase-dependent heat current, and is unique to …
In superconductivity, electrons exhibit unique macroscopic collective quantum behavior that is the key for many modern quantum technologies. This electron behavior stems vastly from coupling to a correlated motion of atoms in the material, as well as from synchronized directional movement that screens external magnetic fields perfectly. Hence, the inter-atomic distance and material geometry are expected to affect fundamental superconductive characteristics. These parameters are tunable with strain, but strain application is hindered by the rigidity of superconductors, which in turn increases a…
Controlling both the amplitude and phase of the quantum order parameter (ψ) in nanostructures is important for next-generation information and communication technologies. The long-range coherence of attractive electrons in superconductors render these materials as a nearly ideal platform for such applications. To-date, control over ψ has remained limited to the macroscopic scale, either by adjusting untunable materials properties, such as film thickness, stoichiometry and homogeneity or by tuning external magnetic fields. Yet, although local tuning of ψ is desired, the lack of electric resista…
Tomogram-based quantifiers of nonclassicality dynamics in Kerr and cubic media
本文提出基于汤姆逊图的非经典性量化方法，用于研究 Kerr 和立方介质中非经典性动态，通过平衡光探测直接获取光学汤姆逊图，避免密度矩阵重建，提供实验可行的非经典性度量。
We numerically solve the Liouville equation for the Tavis Cummings model of multiple spins coupled to a lossless single mode cavity, starting from an initial condition with small numbers of fully polarized spins tipped by a specified angle, and the cavity in its ground Fock state. Time evolution of the magnetizations and cavity states, following small to medium nutation by a classical field, yields a microscopic quantum mechanical picture of radiation damping in magnetic resonance, and the formation of the free induction signal, that is, the transfer of Zeeman energy, via spin coherence, to ca…
Optically levitated nanoparticles have recently emerged as versatile platforms for investigating macroscopic quantum mechanics and enabling ultrasensitive metrology. In this article we theoretically consider two damping regimes of an optically levitated nanoparticle cooled by cavityless parametric feedback. Our treatment is based on a generalized Fokker-Planck equation derived from the quantum master equation presented recently and shown to agree very well with experiment [1]. For low damping, we find that the resulting Wigner function yields the single-peaked oscillator position distribution …
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