Generating two continuous entangled microwave beams using a dc-biased Josephson junction
A. Peugeot, G. Ménard, S. Dambach, M. Westig, B. Kubala, Y. Mukharsky, C. Altimiras, P. Joyez, D. Vion, P. Roche, D. Esteve, P. Milman, J. Leppäkangas, G. Johan… 展开作者
A. Peugeot, G. Ménard, S. Dambach, M. Westig, B. Kubala, Y. Mukharsky, C. Altimiras, P. Joyez, D. Vion, P. Roche, D. Esteve, P. Milman, J. Leppäkangas, G. Johansson, M. Hofheinz, J. Ankerhold, F. Portier
We show experimentally that a dc-biased Josephson junction in series with two microwave resonators emits entangled beams of microwaves leaking out of the resonators. In the absence of a stationary phase reference for characterizing the entanglement of the outgoing beams, we measure second-order coherence functions for proving entanglement up to an emission rate of 2.5 billion photon pairs per second. The experimental results are found in quantitative agreement with theory, proving that the low frequency noise of the dc bias is the main limitation for the coherence time of the entangled beams. This agreement allows us to evaluate the entropy of entanglement of the resonators, and to identify the improvements that could bring this device closer to a useful bright source of entangled microwaves for quantum-technological applications.
We present and analyze a reservoir-engineering approach to stabilizing Fock states in a superconducting microwave cavity which does not require any microwave-frequency control drives. Instead, our system makes use of a Josephson junction biased by a dc voltage which is coupled both to a principle storage cavity and a second auxiliary cavity. Our analysis shows that Fock states can be stabilized with an extremely high fidelity. We also show how the same system can be used to prepare on-demand propagating Fock states, again without the use of microwave pulses.
We analyze the quantum efficiency of a microwave photon detector based on a current-biased Josephson junction. We consider the Jaynes-Cummings Hamiltonian to describe coupling between the photon field and the junction. We then take into account coupling of the junction and the resonator to the environment. We solve the equation of motion of the density matrix of the resonator-junction system to compute the quantum efficiency of the detector as a function of detection time, bias current, and energy relaxation time. Our results indicate that junctions with modest coherence properties can provide…
Engineering multi-photon dissipation with a dc-voltage-biased Josephson junction
École Normale Supérieure de Lyon（里昂高等师范学院）；CNRS（法国国家科学研究中心）；Laboratoire de Physique（物理实验室）；Alice & Bob；Mines Paris（巴黎矿业学院）；Inria（法国国家信息与自动化研究所）；ENS-PSL（巴黎高等师范学院-PSL大学）；Centre Automatique et Systèmes (CAS)（自动系统与中心）；Sorbonne Université（索邦大学）；PSL Research University（PSL研究大学）
Two mesoscopic SQUID rings which are far from each other, are considered. A source of two-mode nonclassical microwaves irradiates the two rings with correlated photons. The Josephson currents are in this case quantum mechanical operators, and their expectation values with respect to the density matrix of the microwaves, yield the experimentally observed currents. Classically correlated (separable) and quantum mechanically correlated (entangled) microwaves are considered, and their effect on the Josephson currents is quantified. Results for two different examples that involve microwaves in numb…
Shot noise in a voltage source changes the character of the quantum (dissipative) phase transition in an ultrasmall Josephson junction: The superconductor-insulator transition transforms into the superconductor-metal transition. In the metallic phase the IV curve probes the voltage distribution generated by shot noise, whereas in the superconducting phase it probes the counting statistics of electrons traversing the noise junction.
We propose a realization of the superconducting diode effect in flux biased superconducting circuits of Josephson junctions. So far the observation of the superconducting diode effect has been limited to rather exotic material platforms. In theoretical proposals, it relied on a non-sinusoidal form of the current phase relation of Josephson junctions. Here, we show how the diode effect can be engineered in superconducting circuits without any such requirements. The only necessary ingredients are standard sinusoidal Josephson junctions and flux bias lines that are readily available in scalable i…
We show experimentally that a dc biased Josephson junction in series with a high-enough impedance microwave resonator emits antibunched photons. Our resonator is made of a simple micro-fabricated spiral coil that resonates at 4.4 GHz and reaches a 1.97 k$Ω$ characteristic impedance. The second order correlation function of the power leaking out of the resonator drops down to 0.3 at zero delay, which demonstrates the antibunching of the photons emitted by the circuit at a rate of 6 $10^7$ photons per second. Results are found in quantitative agreement with our theoretical predictions. This simp…
The interplay of the tunneling transfer of charges and the emission and absorption of light can be investigated in a set-up, where a voltage-biased Josephson junction is placed in series to a microwave cavity. Here, we concentrate on the emission process and show that due to the inherent nonlinearity of the Josephson junction tunneling Cooper-pairs can create a variety of non-classical states of light. Depending on experimental parameters and tuning the device can be described by effective Hamiltonians, indicating specific photon creation mechanisms which lead to strongly bunched or anti-bunch…
We study the dynamics of a quantum superconducting circuit which consists of a Josephson charge qubit, coupled capacitively to a current biased Josephson junction. Under certain conditions, the eigenstates of the qubit and the junction become entangled. We obtain the time evolution of these states in the limit of weak coupling. Rabi oscillations occur, as a result of the spontaneous emission and re-absorption of a single oscillation quantum in the junction. We discuss a possible way to experimentally determine the quantum state of the junction and hence observe the Rabi oscillations.
We demonstrate that a suspended nanowire forming a weak link between two superconductors can be cooled to its motional ground state by a supercurrent flow. The predicted cooling mechanism has its origins in magnetic field induced inelastic tunneling of the macroscopic superconducting phase associated with the junction. Furthermore, we show the voltage-drop over the junction is proportional to the average population of the vibrational modes in the stationary regime, a phenomena which can be used to probe the level of cooling.
Nonequilibrium quasiparticles are ubiquitous in superconducting electronics. These quasiparticles can trap in the internal Andreev bound states of a phase-biased Josephson junction, providing a mechanism for studying their presence and behavior. We characterize a quasiparticle trapping detector device based on a two-junction aluminum nanobridge superconducting quantum interference device incorporated into a transmission-line resonator. When flux-biased, distinct resonant frequencies develop depending on the trapped quasiparticle number. We demonstrate continuous detection of up to 3 trapped qu…
We investigate electromagnetic radiation emitted by a small voltage-biased Josephson junction connected to a superconducting transmission line. At frequencies below the well known emission peak at the Josephson frequency (2eV/h), extra radiation is triggered by quantum fluctuations in the electromagnetic environment. For weak tunneling couplings and typical ohmic transmission lines, the corresponding photon flux spectrum is symmetric around half the Josephson frequency, indicating that the photons are predominately created in pairs. By establishing an input-output formalism for the microwave f…
Josephson current of spin-entangled electrons through the two branches of a SQUID-like structure with two quantum dots exhibits a magnetic-flux response different from the conventional Josephson current. Due to their interference, the period of maximum Josephson current changes from $h/2e$ to $h/e$, which can be used for detecting the Cooper-pair splitting efficiency. The nonlocal spin entanglement provides a quantum mechanical functionale for switching on and off this novel Josephson current, and explicitly a switch is formulated by including a pilot junction. It is shown that the device can …
This work reports a novel time-domain expression for the current-response kernels of a Josephson tunnel junction between BCS superconductors with in general different energy gaps, and its use to simulate the classical dynamics of such junctions. The simulations show a dynamic regime characterized by the resonance between the Josephson oscillations and the gap oscillations in the asymptotics of the current kernels that has not been studied previously. The resonance manifests itself as a hysteresis in the dc current-voltage characteristics of the current-biased junctions in the voltage range abo…
When connecting a voltage-biased Josephson junction in series to several microwave cavities, a Cooper-pair current across the junction gives rise to a continuous emission of strongly correlated photons into the cavity modes. Tuning the bias voltage to the resonance where a single Cooper pair provides the energy to create an additional photon in each of the cavities, we demonstrate the entangling nature of these creation processes by simple witnesses in terms of experimentally accessible observables. To characterize the entanglement properties of the such created quantum states of light to the …
We study a double quantum dot each dot of which is tunnel-coupled to superconducting leads. In the Coulomb blockade regime, a spin-dependent Josephson coupling between two superconductors is induced, as well as an antiferromagnetic Heisenberg exchange coupling between the spins on the double dot which can be tuned by the superconducting phase difference. We show that the correlated spin states-singlet or triplets-on the double dot can be probed via the Josephson current in a dc-SQUID setup.
We investigate the coherent energy and thermal transport in a temperature-biased long Josephson tunnel junction, when a Josephson vortex, i.e., a soliton, steadily drifts driven by an electric bias current. We demonstrate that thermal transport through the junction can be controlled by the bias current, since it determines the steady-state velocity of the drifting soliton. We study the effects on thermal transport of the damping affecting the soliton dynamics. In fact, a soliton locally influences the power flowing through the junction and can cause the variation of the temperature of the devi…
We investigate the behavior of a Josephson junction consisting of a ferromagnetic insulator-superconductor (FI-S) bilayer tunnel-coupled to a superconducting electrode. We show that the Josephson coupling in the structure is strenghtened by the presence of the spin-splitting field induced in the FI-S bilayer. Such strenghtening manifests itself as an increase of the critical current $I_c$ with the amplitude of the exchange field. Furthermore, the effect can be strongly enhanced if the junction is taken out of equilibrium by a temperature bias. We propose a realistic setup to assess experimenta…
Periodic in time spin-Hall current and spin polarization induced by a dc electric bias has been calculated in a superconductor-normal 2DEG-superconductor (SNS) Josephson junction. We assumed that the band energies of electrons in the normal system are splitted due to Rashba spin-orbit coupling. The transport parameters have been calculated within the diffusion approximation and using perturbation expansion over a small SN contact transparency. We found out that in contrast to the stationary Josephson effect, the spin-Hall current does not turn to zero. Besides a direct proximity effect caused …
We calculate the current-voltage (I-V) characteristic of a Josephson junction containing a resonant level in the weakly coupled regime (resonance width small compared to the superconducting gap). The phase $ϕ$ across the junction becomes time dependent in response to a DC current bias. Rabi oscillations in the Andreev levels produce a staircase I-V characteristic. The number of voltage steps counts the number of Rabi oscillations per $2π$ increment of $ϕ$, providing a way to probe the coherence of the qubit in the absence of any external AC driving. The phenomenology is the same as the "Majora…
The dc transport properties of long arrays of small Al Josephson junctions, biased through on-chip Cr resistors, are studied. The IV-characteristics show a large Coulomb threshold for current as well as negative-slope regions indicating the regime of autonomous Bloch oscillations up to rather high frequencies of f = I/2e ~1 GHz, comparable to those reported by other groups for single junctions. On the other hand, a small depth of the back-bending implies a low duty cycle and a broad spectrum of the oscillations, which we attribute to the insufficiently high impedance of the bias resistors. A s…
Motivated by recent experiments, where a voltage biased Josephson junction is placed in series with a resonator, the classical dynamics of the circuit is studied in various domains of parameter space. This problem can be mapped onto the dissipative motion of a single degree of freedom in a nonlinear time-dependent potential, where in contrast to conventional settings the nonlinearity appears in the driving while the static potential is purely harmonic. For long times the system approaches steady states which are analyzed in the underdamped regime over the full range of driving parameters inclu…
We analyze the current-biased Shapiro experiment in a Josephson junction formed by two one-dimensional nanowires featuring Majorana fermions. Ideally, these junctions are predicted to have an unconventional $4π$-periodic Josephson effect and thus only Shapiro steps at even multiples of the driving frequency. Taking additionally into account overlap between the Majorana fermions, due to the finite length of the wire, renders the Josephson junction conventional for any dc-experiments. We show that probing the current-phase relation in a current biased setup dynamically decouples the Majorana fer…
Using a superconducting circuit, the Josephson mixer, we demonstrate the first experimental realization of spatially separated two-mode squeezed states of microwave light. Driven by a pump tone, a first Josephson mixer generates, out of quantum vacuum, a pair of entangled fields at different frequencies on separate transmission lines. A second mixer, driven by a $π$-phase shifted copy of the first pump tone, recombines and disentangles the two fields. The resulting output noise level is measured to be lower than for vacuum state at the input of the second mixer, an unambiguous proof of entangl…
We study a planar Josephson junction under an applied DC voltage bias in the presence of an in-plane magnetic field. Upon tuning the bias voltage across the junction, $V_{\rm J}$, the two ends of the junction are shown to simultaneously host both $0$- and $π$-Majorana modes. These modes can be probed using either a Scanning-Tunneling-Microscopy measurement or through resonant Andreev tunneling from a lead coupled to the junction. While these modes are mostly bound to the junction's ends, they can hybridize with the bulk by absorbing or emitting photons. We analyze this process both numerically…
We theoretically study the behavior of the critical current of a thermally-biased tunnel Josephson junction with a particular design, in which the electrodes of the junction are enclosed in two different superconducting loops pierced by independent magnetic fluxes. In this setup, the superconducting gaps can be modified independently through the magnetic fluxes threading the loops. We investigate the response of the device as a function of the magnetic fluxes, by changing the asymmetry parameter, i.e., the ratio between the zero-temperature superconducting gaps $δ=Δ_{10}/Δ_{20}$, and the tempe…
By coupling a superconducting weak link to a microwave resonator, recent experiments probed the spectrum and achieved the quantum manipulation of Andreev states in various systems. However, the quantitative understanding of the response of the resonator to changes in the occupancy of the Andreev levels, which are of fermionic nature, is missing. Here, using Bogoliubov-de Gennes formalism to describe the weak link and a general formulation of the coupling to the resonator, we calculate the shift of the resonator frequency as a function of the levels occupancy and describe how transitions are in…
In a Josephson junction (JJ), Cooper pairs are transported via Andreev bound states (ABSs) between superconductors. The ABSs in the weak link of multi-terminal (MT) JJs can coherently hybridize two Cooper pairs among different superconducting electrodes, resulting in the Cooper quartet (CQ) involving four fermions entanglement. The energy spectrum of these CQ-ABS can be controlled by biasing MT-JJs due to the AC Josephson effect. Here, using gate tunable four-terminal graphene JJs complemented with a flux loop, we construct CQs with a tunable spectrum. The critical quartet supercurrent exhibit…
We explore the similarities and differences between simple theoretical models developed to describe the quantum optical micromaser and Josephson-photonics devices. Whilst the micromaser has long been recognised as an important model for the dynamics of open quantum systems far from equilibrium, so-called Josephson-photonics devices are a recently developed form of superconducting quantum circuit in which the quantum transport of charges through a voltage-biased Josephson junction drives the production of photons in a microwave resonator.
We study the dynamics of a quantum superconducting circuit which is the analogue of an atom in a high-Q cavity. The circuit consists of a Josephson charge qubit coupled to a superconducting resonator. The charge qubit can be treated as a two level quantum system whose energy separation is split by the Josephson energy $E_j$. The superconducting resonator in our proposal is the analogue of a photon box and is described by a quantum harmonic oscillator with characteristic frequency $ω_r$. The coupling between the charge qubit and the resonator is realized by a coupling capacitance $C_c$. We have…
Theory of non-stationary coherent effects is developed for superconductor-normal-superconductor (SNS) structures with relatively strong normal scattering on S/N interfaces (interface resistance is large compared to intrinsic resistance of N metal). Analitical expressions are found for the time-dependent anomalous Green functions induced in the N region under the fixed-voltage-bias. The amplitude of the current oscillations is determined in non-equilibrium conditions. Non-stationary correction to the distribution function is calculated in high-temperature limit and found to be slowly decreasing…
We theoretically investigate an opportunity to implement a source of highly spin-polarized ac current on the basis of superconductor/weak ferromagnet/superconductor (SFS) voltage-biased junction in the regime of essential proximity effect and calculate the current flowing through the probe electrode tunnel coupled to the ferromagnetic interlayer region. It is shown that while the polarization of the dc current component is generally small in case of weak exchange field of the ferromagnet, there is an ac component of the current in the system. This ac current is highly spin-polarized and entire…
An all-superconducting bijunction consists of a central superconductor contacted to two lateral superconductors, such that non-local crossed Andreev reflection is operating. Then new correlated transport channels for the Cooper pairs appear in addition to those of separated conventional Joseph- son junctions. We study this system in a configuration where the superconductors are connected through gate-controllable quantum dots. Multipair phase-coherent resonances and phase-dependent multiple Andreev reflections are both obtained when the voltages of the lateral superconductors are commensurate,…
The Josephson quasiparticle (JQP) cycle in a voltage-biased superconducting single-electron transistor (SSET) combines coherent Cooper pair tunneling with incoherent quasiparticle decay. We have measured the influence of current flow through an independently-biased SSET on the JQP cycle when the two SSET's have a strong mutual capacitive coupling. We find, among other effects, that the JQP current in one SSET is enhanced by the presence of a quasiparticle current in the other SSET. A simplified model of the coupled-SSET system is presented which reproduces the enhancement effect.
We present a simple model for multiphoton transitions between the quasi-bound states of a current-driven Josephson junction. The transitions are induced by applying an ac voltage with controllable frequency and amplitude across the junction. The voltage induces transitions when the ac frequency equals n times the splitting between the ground and first excited quasi-bound state of the junction. We calculate the transition matrix elements as functions of the dc bias current I, and the frequency and amplitude of the ac voltage, for representative junction parameters. We also calculate the frequen…
A three-terminal Josephson junction consists of three superconductors coupled coherently to a small nonsuperconducting island, such as a diffusive metal, a single or double quantum dot. A specific resonant single quantum dot three-terminal Josephson junction $(S_a,S_b,S_c)$ biased with voltages $(V,-V,0)$ is considered, but the conclusions hold more generally for resonant semi-conducting quantum wire set-ups. A simple physical picture of the steady state is developed, using Floquet theory. It is shown that the equilibrium Andreev bound states (for $V=0$) evolve into nonequilibrium Floquet-Wann…
We investigate the proximity effect in junctions between $N=3$ superconductors under commensurate voltage bias. The bias is chosen to highlight the role of transport processes that exchange multiple Cooper pairs coherently between more than two superconductors. Such non-local processes can be studied in the dc response, where local transport processes do not contribute. We focus on the proximity-induced normal density of states that we investigate in a wide parameter space. We reveal the presence of deep and highly tunable pseudogaps and other rich structures. These are due to a static proximi…
We propose a scheme to generate and detect entanglement between charge states in superconducting nanocircuits. We discuss different procedures to discriminate such entanglement from classical correlations. The case of maximally entangled states of two and three coupled Josephson junctions is discussed as example.
Deep theoretical understanding of the electrical response of Josephson junctions is indispensable regarding both recent discoveries of new kinds of superconductivity and technological advances such as superconducting quantum computers. Here, we study the microscopic theory of the DC current-biased $I$-$V$ characteristics of Josephson tunnel junctions. We derive an analytical formula of the $I$-$V$ characteristics of generic junctions. We identify subharmonics of the $I$-$V$ characteristics and their underlying mechanism as the feedback effect of intrinsic AC currents generated by voltage pulse…
We demonstrate how robust entanglement of quantum dot molecular system in a voltage controlled junction can be generated. To improve the quantum information characteristics of this system, we propose an applicable protocol which contains the implementation of asymmetric quantum dots as well as engineering reservoirs. Quantum dots with tunable energy barriers can provide asymmetric coupling coefficients which can be tuned by gap voltages. Also by engineering reservoirs, superconductors can be used as leads in a biased-voltage junction. The high-controllability characteristics of system supplies…
We propose a scheme to implement the two-qubit quantum phase gate with Josephson-junction charge qubits in a thermal cavity. In this scheme, the photon-number-dependent parts in the time evolution operator are canceled at the special time. Thus the scheme is insensitive to the thermal field. We also demonstrate that the scheme can be used to generate maximally entangled state of many Josephson-junction charge qubits
We demonstrate that two coupled Bose-Einstein condensates (BEC) at zero temperature can be used to realize a qubit which is the counterpart of Josephson charge qubits. The two BEC are weakly coupled and confined in an asymmetric double-well trap. When the "charging energy" of the system is much larger than the Josephson energy and the system is biased near a degeneracy point, the two BEC represent a qubit with two states differing only by one atom. The realization of the BEC qubits in realistic BEC experiments is briefly discussed.
We describe a microwave photon counter based on the current-biased Josephson junction. The junction is tuned to absorb single microwave photons from the incident field, after which it tunnels into a classically observable voltage state. Using two such detectors, we have performed a microwave version of the Hanbury Brown and Twiss experiment at 4 GHz and demonstrated a clear signature of photon bunching for a thermal source. The design is readily scalable to tens of parallelized junctions, a configuration that would allow number-resolved counting of microwave photons.
The two-level systems (TLSs) naturally occurring in Josephson junctions constitute a major obstacle for the operation of superconducting phase qubits. Since these TLSs can possess remarkably long decoherence times, we show that such TLSs can themselves be used as qubits, allowing for a well controlled initialization, universal sets of quantum gates, and readout. Thus, a single current-biased Josephson junction (CBJJ) can be considered as a multiqubit register. It can be coupled to other CBJJs to allow the application of quantum gates to an arbitrary pair of qubits in the system. Our results in…
