We demonstrate theoretically the noise-stimulated enhancement of quantum coherence in a superconducting flux qubit. First, an external classical noise can increase the off-diagonal components of the qubit density matrix. Second, in the presence of noise, the Rabi oscillations survive for times significantly longer than the Rabi decay time in a noiseless system. These Rabi oscillations appear as a modulation of the forced response of the qubit to the ac driving field. These effects can be considered as a manifestation of quantum stochastic resonance and are relevant to experimental techniques, such as Rabi spectroscopy.
Under resonant irradiation, a quantum system can undergo coherent (Rabi) oscillations in time. We report evidence for such oscillations in a _continuously_ observed three-Josephson-junction flux qubit, coupled to a high-quality tank circuit tuned to the Rabi frequency. In addition to simplicity, this method of_Rabi spectroscopy_ enabled a long coherence time of about 2.5 microseconds, corresponding to an effective qubit quality factor \~7000.
The qubit Rabi oscillations are known to be non-decaying (though with a fluctuating phase) if the qubit is continuously monitored in the weak-coupling regime. In this paper we propose an experiment to demonstrate these persistent Rabi oscillations via low-frequency noise correlation. The idea is to measure a qubit by two detectors, biased stroboscopically at the Rabi frequency. The low-frequency noise depends on the relative phase between the two combs of biasing pulses, with a strong increase of telegraph noise in both detectors for the in-phase or anti-phase combs. This happens because of se…
We present a theoretical study of a quantum regime of the resistive (whirling) state of dc driven anisotropic single plaquette containing three small Josephson junctions. The current-voltage characteristics of such a system display resonant steps that are due to the resonant interaction between the time dependent Josephson current and the excited electromagnetic oscillations (EOs). The voltage positions of the resonances are determined by the quantum interband transitions of EOs. We show that in the quantum regime as the system is driven on the resonance, coherent Rabi oscillations between the…
Mach-Zehnder atom interferometry requires hold-time phase-squeezing to attain readout accuracy below the standard quantum limit. This increases its sensitivity to phase-diffusion, restoring shot-noise scaling of the optimal signal-to-noise ratio, $s_o$, in the presence of interactions. The contradiction between the preparations required for readout accuracy and robustness to interactions, is removed by monitoring Rabi-Josephson oscillations instead of relative-phase oscillations during signal acquisition. Optimizing $s_o$ with a Gaussian squeezed input, we find that hold-time number squeezing …
The act of measurement bridges the quantum and classical worlds by projecting a superposition of possible states into a single, albeit probabilistic, outcome. The time-scale of this "instantaneous" process can be stretched using weak measurements so that it takes the form of a gradual random walk towards a final state. Remarkably, the interim measurement record is sufficient to continuously track and steer the quantum state using feedback. We monitor the dynamics of a resonantly driven quantum two-level system -- a superconducting quantum bit --using a near-noiseless parametric amplifier. The …
Circuit quantum electrodynamics (QED) studies the interaction of artificial atoms, open transmission lines and electromagnetic resonators fabricated from superconducting electronics. While the theory of an artificial atom coupled to one mode of a resonator is well studied, considering multiple modes leads to divergences which are not well understood. Here, we introduce a first-principles model of a multimode resonator coupled to a Josephson junction atom. Studying the model in the absence of any cutoff, in which the coupling rate to mode number $n$ scales as $\sqrt{n}$ for $n$ up to $\infty$, …
We investigate the driven quantum phase transition between the oscillating motion and the classical nearly free rotations of the Josephson pendulum coupled to a harmonic oscillator in the presence of dissipation. We refer to this as the Josephson-Rabi model. This model describes the standard setup of circuit quantum electrodynamics, where typically a transmon device is embedded in a superconducting cavity. We find that by treating the system quantum mechanically this transition occurs at higher drive powers than expected from an all-classical treatment, which is a consequence of the quasiperio…
We perform a detailed field theoretical study of nonequilibrium Josephson oscillations between interacting Bose-Einstein condensates confined in a finite-size double-well trap. We find that the Josephson junction can sustain multiple undamped Josephson oscillations up to a characteristic time scale $τ_c$ without quasipartcles being excited in the system. This may explain recent related experiments. At larger times the dynamics of the junction is governed by fast Rabi oscillations between the descrete quasiparticle levels. We predict that a selftrapped BEC state will be destroyed by these Rabi …
We discuss the relaxation and dephasing rates that result from the control and the measurement setup itself in experiments on Josephson persistent-current qubits. For control and measurement of the qubit state, the qubit is inductively coupled to electromagnetic circuitry. We show how this system can be mapped on the spin-boson model, and how the spectral density of the bosonic bath can be derived from the electromagnetic impedance that is coupled to the qubit. Part of the electromagnetic environment is a measurement apparatus (DC-SQUID), that is permanently coupled to the single quantum syste…
We analyze the behavior of systems of two and three qubits made by Josephson junctions, treated in the two level approximation, driven by a radiation mode in a cavity. The regime we consider is a strong coupling one recently experimentally reached for a single junction. Rabi oscillations are obtained with the frequency proportional to integer order Bessel functions in the limit of a large photon number, similarly to the case of the single qubit. A selection rule is derived for the appearance of Rabi oscillations. A quantum amplifier built with a large number of Josephson junctions in a cavity …
We present a stability analysis of an interacting two-species Bose-Einstein condensate driven by a quantized field in the semi-classical limit. Transitions from Rabi to Josephson dynamics are identified depending on both the inter-atomic interaction to field-condensate coupling ratio and the ratio between the total excitation number and the condensate size. The quantized field is found to produce asymmetric dynamics for symmetric initial conditions for both Rabi and Josephson oscillations.
We report single-shot readout of a superconducting flux qubit by using a flux-driven Josephson parametric amplifier (JPA). After optimizing the readout power, gain of the JPA and timing of the data acquisition, we observe the Rabi oscillations with a contrast of 74% which is mainly limited by the bandwidth of the JPA and the energy relaxation of the qubit. The observation of quantum jumps between the qubit eigenstates under continuous monitoring indicates the nondestructiveness of the readout scheme.
Achieving individual qubit readout is a major challenge in the development of scalable superconducting quantum processors. We have implemented the multiplexed readout of a four transmon qubit circuit using non-linear resonators operated as Josephson bifurcation amplifiers. We demonstrate the simultaneous measurement of Rabi oscillations of the four transmons. We find that multiplexed Josephson bifurcation is a high-fidelity readout method, the scalability of which is not limited by the need of a large bandwidth nearly quantum-limited amplifier as is the case with linear readout resonators.
We study coherent phonon oscillations and tunneling between two coupled nonlinear nanomechanical resonators. We show that the coupling between two nanomechanical resonators creates an effective phonon Josephson junction which exhibits two different dynamical behaviors: Josephson oscillation (phonon-Rabi oscillation) and macroscopic self-trapping (phonon blockade). Self-trapping originates from mechanical nonlinearities, meaning that when the nonlinearity exceeds its critical value, the energy exchange between the two resonators is suppressed, and phonon-Josephson oscillations between them are …
We proposed a scheme to demonstrate macroscopic quantum jumps in a superconducting phase qubit coupled to a microscopic two-level system in the Josephson tunnel junction. Irradiated with suitable microwaves, the Rabi oscillations of the qubit exhibit signatures of quantum jumps: a random telegraph signal with long intervals of intense macroscopic quantum tunneling events (bright periods) interrupted by the complete absence of tunneling events (dark periods). An analytical model was developed to describe the width of the dark periods quantitatively. The numerical simulations indicate that our a…
A quantum mechanical analysis of the Josephson phase escape in the presence of both dc and ac bias currents is presented. We find that the potential barrier for the escape of the phase is effectively suppressed as the resonant condition occurs, i.e. when the frequency $ω$ of the ac bias matches the Josephson junction energy level separation. This effect manifests itself by a pronounced drop in the dependence of the switching current $I_s$ on the power $W$ of the applied microwave radiation and by a peculiar double-peak structure in the switching current distribution $P(I_s)$. The developed the…
We present a quantum computing scheme with atomic Josephson junction arrays. The system consists of a small number of atoms with three internal states and trapped in a far-off resonant optical lattice. Raman lasers provide the "Josephson" tunneling, and the collision interaction between atoms represent the "capacitive" couplings between the modes. The qubit states are collective states of the atoms with opposite persistent currents. This system is closely analogous to the superconducting flux qubit. Single qubit quantum logic gates are performed by modulating the Raman couplings, while two-qub…
We investigate the existence of the $macroscopic$ $quantum$ $phase$ in trapped ultracold quantum degenerate gases, such as Bose-Einstein condensate, in an asymmetrical two-dimensional magnetic lattice. We show the key to adiabatically control the tunneling in the new two-dimensional magnetic lattice by means of external magnetic bias fields. The macroscopic quantum phase signature is identified as a Rabi-like oscillation when solving the system of coupled time-dependent differential equations, described here by the Boson Josephson Junctions (BJJs). In solving the system of the BJJs we used an …
A battery is a classical apparatus which converts a chemical reaction into a persistent voltage bias able to power electronic circuits. Similarly, a phase battery is a quantum equipment which provides a persistent phase bias to the wave function of a quantum circuit. It represents a key element for quantum technologies based on quantum coherence. Unlike the voltage batteries, a phase battery has not been implemented so far, mainly because of the natural rigidity of the quantum phase that, in typical quantum circuits, is imposed by the parity and time-reversal symmetry constrains. Here we repor…
Two coupled-cavity systems, or "photonic dimers", are efficient test-beds for both fundamental optics -the realization of quantum correlated states, Josephson physics, and so forth-, and applications such as optical flip-flop memories. In this work we report on the first observation of nonlinear mode interaction in a photonic dimer formed by two semiconductor photonic crystal coupled nanolasers. For this, we investigate energy transfer between hybrid modes, which manifests as a switching from the blue-detuned (bonding) to the red-detuned (anti-bonding) modes. An mean-field model allows us to e…
A two-level atom interacting with a single radiation mode is considered, without the rotating-wave approximation, in the strong coupling regime. It is shown that, in agreement with the recent results on Rabi oscillations in a Josephson junction (Y. Nakamura, Yu. A. Pashkin and J. S. Tsai, Phys. Rev. Lett. {\bf 87}, 246601 (2001)), the Rabi frequency is indeed proportional to first kind integer order Bessel functions in the limit of a large number of photons and the dressed states are macroscopic quantum superposition states. To approach this problem analytically use is made of the dual Dyson s…
The parametric phase-locked oscillator (PPLO), also known as a parametron, is a resonant circuit in which one of the reactances is periodically modulated. It can detect, amplify, and store binary digital signals in the form of two distinct phases of self-oscillation. Indeed, digital computers using PPLOs based on a magnetic ferrite ring or a varactor diode as its fundamental logic element were successfully operated in 1950s and 1960s. More recently, basic bit operations have been demonstrated in an electromechanical resonator, and an Ising machine based on optical PPLOs has been proposed. Here…
We investigate the quantum dynamics of a Cooper-pair box with a superconducting loop in the presence of a nonclassical microwave field. We demonstrate the existence of Rabi oscillations for both single- and multi-photon processes and, moreover, we propose a new quantum computing scheme (including one-bit and conditional two-bit gates) based on Josephson qubits coupled through microwaves.
We propose an active mechanism for coupling the quantized mode of a nanomechanical resonator to the persistent current in the loop of a superconducting Josephson junction (or phase slip) flux qubit. This coupling is independently controlled by an external coupling magnetic field. The whole system forms a novel solid-state cavity quantum electrodynamics (QED) architecture in the strong coupling limit. This architecture can be used to demonstrate quantum optics phenomena and coherently manipulate the qubit for quantum information processing. The coupling mechanism is applicable for more generali…
We explore the interplay between tunneling and interatomic interactions in the dynamics of a bosonic Josephson junction. We tune the scattering length of an atomic $^{39}$K Bose-Einstein condensate confined in a double-well trap to investigate regimes inaccessible to other superconducting or superfluid systems. In the limit of small-amplitude oscillations, we study the transition from Rabi to plasma oscillations by crossing over from attractive to repulsive interatomic interactions. We observe a critical slowing down in the oscillation frequency by increasing the strength of an attractive inte…
In circuit quantum electrodynamics (circuit QED), an artificial "circuit atom" can couple to a quantized microwave radiation much stronger than its real atomic counterpart. The celebrated quantum Rabi model describes the simplest interaction of a two-level system with a single-mode boson field. When the coupling is large enough, the bare multilevel structure of a realistic circuit atom cannot be ignored even if the circuit is strongly anharmonic. We explored this situation theoretically for flux (fluxonium) and charge (Cooper pair box) type multi-level circuits tuned to their respective flux/c…
Superconducting circuits extensively rely on the Josephson junction as a nonlinear electronic element for manipulating quantum information and mediating photon interactions. Despite continuing efforts in designing anharmonic Josephson circuits with improved coherence times, the best photon lifetimes have been demonstrated in microwave cavities. Nevertheless, architectures based on quantum memories need a qubit element for addressing these harmonic modules at the cost of introducing additional loss channels and limiting process fidelities. This work focuses on tailoring the oscillator Hilbert s…
Making a system state follow a prescribed trajectory despite fluctuations and errors commonly consists in monitoring an observable (temperature, blood-glucose level...) and reacting on its controllers (heater power, insulin amount ...). In the quantum domain, there is a change of paradigm in feedback since measurements modify the state of the system, most dramatically when the trajectory goes through superpositions of measurement eigenstates. Here, we demonstrate the stabilization of an arbitrary trajectory of a superconducting qubit by measurement based feedback. The protocol benefits from th…
We describe a chip-based, solid-state analogue of cavity-QED utilizing acoustic phonons instead of photons. We show how long-lived and tunable acceptor impurity states in silicon nanomechanical cavities can play the role of a matter non-linearity for coherent phonons just as, e.g., the Josephson qubit plays in circuit-QED. Both strong coupling (number of Rabi oscillations ~ 100) and strong dispersive coupling (0.1-2 MHz) regimes can be reached in cavities in the 1-20 GHz range, enabling the control of single phonons, phonon-phonon interactions, dispersive phonon readout of the acceptor qubit, …
We present the design of a superconducting qubit that has circulating currents of opposite sign as its two states. The circuit consists of three nano-scale aluminum Josephson junctions connected in a superconducting loop and controlled by magnetic fields. The advantages of this qubit are that it can be made insensitive to background charges in the substrate, the flux in the two states can be detected with a SQUID, and the states can be manipulated with magnetic fields. Coupled systems of qubits are also discussed as well as sources of decoherence.
We construct a minimal circuit, based on the top-transmon design, to rotate a qubit formed out of four Majorana zero-modes at the edge of a two-dimensional topological insulator. Unlike braiding operations, generic rotations have no topological protection, but they do allow for a full characterization of the coherence times of the Majorana qubit. The rotation is controlled by variation of the flux through a pair of split Josephson junctions in a Cooper pair box, without any need to adjust gate voltages. The Rabi oscillations of the Majorana qubit can be monitored via oscillations in the resona…
We have implemented a resonant circuit that uses a SQUID as a flux-sensitive Josephson inductor for qubit readout. In contrast to the conventional switching current measurement that generates undesired quasi-particles when the SQUID switches to the voltage state, our approach keeps the readout SQUID biased along the supercurrent branch during the measurement. By incorporating the SQUID inductor in a high-Q resonant circuit, we can distinguish the two flux states of a niobium persistent-current (PC) qubit by observing a shift in the resonant frequency of both the magnitude and the phase spectra…
We derive the Hamiltonian of a superconducting circuit that comprises a single-Josephson-junction flux qubit inductively coupled to an LC oscillator, and we compare the derived circuit Hamiltonian with the quantum Rabi Hamiltonian, which describes a two-level system coupled to a harmonic oscillator. We show that there is a simple, intuitive correspondence between the circuit Hamiltonian and the quantum Rabi Hamiltonian. While there is an overall shift of the entire spectrum, the energy level structure of the circuit Hamiltonian up to the seventh excited states can still be fitted well by the q…
The microwave absorption and noise caused by quantum two-level systems (TLS) dramatically suppress the coherence in Josephson junction qubits that are promising candidates for a quantum information applications. Microwave absorption by TLSs is not clearly understood yet because of the complexity of their interactions leading to the spectral diffusion. Here, the theory of the non-linear absorption in the presence of spectral diffusion is developed using the generalized master equation formalism. The theory predicts that the linear absorption regime holds while a TLS Rabi frequency is smaller th…
We investigate theoretically the quantum vacuum properties of a chain of $N$ superconducting Josephson atoms inductively coupled to a transmission line resonator. We derive the quantum field Hamiltonian for such circuit-QED system, showing that, due to the type and strength of the interaction, a quantum phase transition can occur with a twice degenerate quantum vacuum above a critical coupling. In the finite-size case, the degeneracy is lifted, with an energy splitting decreasing exponentially with increasing values of $g^2 N^2$, where $g$ is the dimensionless vacuum Rabi coupling per artifici…
We add quantum fluctuations to a classical period-doubling Hamiltonian time crystal, replacing the $N$ classical interacting angular momenta with quantum spins of size $l$. The full permutation symmetry of the Hamiltonian allows a mapping to a bosonic model and the application of exact diagonalization for quite large system size. In the thermodynamic limit $N\to\infty$ the model is described by a system of Gross-Pitaevskii equations whose classical-chaos properties closely mirror the finite-$N$ quantum chaos. For $N\to\infty$, and $l$ finite, Rabi oscillations mark the absence of persistent pe…
We formulate a semiclassical approach to study the dynamics of coherence loss and revival in a Bose-Josephson dimer. The phase-space structure of the bi-modal system in the Rabi, Josephson, and Fock interaction regimes, is reviewed and the prescription for its WKB quantization is specified. The local density of states (LDOS) is then deduced for any given preparation from its semiclassical projection onto the WKB eigenstates. The LDOS and the non-linear variation of its level-spacing are employed to construct the time evolution of the initial preparation and study the temporal fluctuations of i…
The future development of quantum information using superconducting circuits requires Josephson qubits with long coherence times combined to a high-delity readout. Major progress in the control of coherence has recently been achieved using circuit quantum electrodynamics (cQED) architectures, where the qubit is embedded in a coplanar waveguide resonator (CPWR) which both provides a well controlled electromagnetic environment and serves as qubit readout. In particular a new qubit design, the transmon, yields reproducibly long coherence times. However, a high-delity single-shot readout of the tr…
We review recent developments concerning non-equilibrium quantum dynamics and many-body physics with light, in superconducting circuits and Josephson analogues. We start with quantum impurity models summarizing the effect of dissipation and of driving the system. We mention theoretical and experimental efforts to characterize these non-equilibrium quantum systems. We show how Josephson junction systems can implement the equivalent of the Kondo effect with microwave photons. The Kondo effect is characterized by a renormalized light-frequency and a peak in the Rayleigh elastic transmission of a …
The future development of quantum information using superconducting circuits requires Josephson qubits [1] with long coherence times combined to a high-fidelity readout. Major progress in the control of coherence has recently been achieved using circuit quantum electrodynamics (cQED) architectures [2, 3], where the qubit is embedded in a coplanar waveguide resonator (CPWR) which both provides a well controlled electromagnetic environment and serves as qubit readout. In particular a new qubit design, the transmon, yields reproducibly long coherence times [4, 5]. However, a high-fidelity single-…
We replace the Josephson junction defining a three-junction flux qubit's properties with a tunable direct current superconducting quantum interference devices (DC-SQUID) in order to tune the qubit gap during the experiment. We observe different gaps as a function of the external magnetic pre-biasing field and the local magnetic field through the DC-SQUID controlled by high-bandwidth on chip control lines. The persistent current and gap behavior correspond to numerical simulation results. We set the sensitivity of the gap on the control lines during the sample design stage. With a tuning range …
We describe a simple, practical scheme for generating multi-qubit W states in resonator-based architectures, in which N Josephson phase qubits are capacitively coupled to a common resonator bus. The entire control sequence consists of three pulses: a local Rabi pulse that excites a single qubit in the circuit; a coupling pulse that transfers the qubit excitation to the resonator bus; and the main, entangling operation that simultaneously couples the bus to all N qubits. If the qubit-resonator coupling strength g is much smaller than the qubit energy splitting, the system initially excited into…
