Suppression of interference by quantum fluctuations in a Josephson interferometer with a single small junction

The geometric inductance of a single-junction interferometer at which quantum fluctuations suppress interference and the Coulomb blockade of Cooper pairs is observed is found.     

Quantum electrodynamic fluctuations of the macroscopic Josephson phase

We study the equilibrium dynamics of the relative phase in a superconducting Josephson link taking into account the quantum fluctuations of the electromagnetic vacuum. The photons act as a superohmic heat bath on the relative Cooper pair number and thus, indirectly, on the macroscopic phase difference φ. This leads to an enhancement of the mean square 〈φ²〉 that adds to the spread due to the Coulomb interaction carried by the longitudinal electromagnetic field. We also include the interaction with the electronic degrees of freedom due to quasiparticle tunneling, which couple to the phase and only indirectly to the particle number. The simultaneous inclusion of both the radiation field fluctuations and quasiparticle tunneling leads to a novel type of particle-bath Hamiltonian in which the quantum particle couples through its position and momentum to two independent bosonic heat baths. We study the interplay between the two mechanisms in the present context and find interference contributions to the quantum fluctuations of the phase. We explore the observability of the QED effects discussed here.     

Quantum Properties of a Single Beam Splitter

When a single beam-splitter receives two beams of bosons described by Fock states (Bose-Einstein condensates at very low temperatures), interesting generalizations of the two-photon Hong-Ou-Mandel effect take place for larger number of particles. The distributions of particles at two detectors behind the beam splitter can be understood as resulting from the combination of two effects, the spontaneous phase appearing during quantum measurement, and the quantum angle. The latter introduces quantum “population oscillations”, which can be seen as a generalized Hong-Ou-Mandel effect, although they do not always correspond to even-odd oscillations.     

Superconducting proximity effect in interacting quantum dots revealed by shot noise

We study the full counting statistics of charge transport through a quantum dot tunnel coupled to one normal and one superconducting lead with a large superconducting gap. As a function of the level detuning, there is a crossover from a regime with strong superconducting correlations in the quantum dot to a regime in which the proximity effect on the quantum dot is suppressed. We analyze the current fluctuations of this crossover in the shot-noise regime. In particular, we predict that the full counting statistics changes from Poissonian with charge 2e, typical for Cooper pairs, to Poissonian with charge e, when the superconducting proximity effect is present. Thus, the onset of the superconducting proximity effect is revealed by the reduction of the Fano factor from 2 to 1.     

Mesoscopic Josephson effect

In the classical Josephson effect the phase difference across the junction is well defined, and the supercurrent is reduced only weakly by phase diffusion. For mesoscopic junctions with small capacitance the phase undergoes large quantum fluctuations, and the current is also decreased by Coulomb blockade effects. We discuss the behavior of the current–voltage characteristics in a large range of parameters comprising the phase diffusion regime with coherent Josephson current as well as the supercurrent peak due to incoherent Cooper pair tunneling in the Coulomb blockade regime.     

约瑟夫森器件中的宏观量子现象及超导量子计算

超导体中的电子结成库珀对，凝聚到可以用一个宏观波函数来描绘的能量基态，该波函数的位相是代表了成百万库珀对集体运动的宏观变量．以约瑟夫森结为基础元件的超导约瑟夫森器件，使人们能够控制并测量一个超导体的位相和库珀对数目，因此是研究宏观量子现象的理想系统．文章回顾了约瑟夫森器件中的宏观量子现象研究的发展历程，介绍了当前超导约瑟夫森器件在量子计算中的重要应用，并对它们的未来作了简要的展望．     

One-shot quantum measurement using a hysteretic dc SQUID

We propose a single shot quantum measurement to determine the state of a Josephson charge quantum bit (qubit). The qubit is a Cooper pair box and the measuring device is a two junction superconducting quantum interference device (dc SQUID). This coupled system exhibits a close analogy with a Rydberg atom in a high Q cavity, except that in the present device we benefit from the additional feature of escape from the supercurrent state by macroscopic quantum tunneling, which provides the final readout. We test the feasibility of our idea against realistic experimental circuit parameters and by analyzing the phase fluctuations of the qubit.     

Superconducting tetrahedral quantum bits

We propose a design for a qubit with four superconducting islands in the topology of a symmetric tetrahedron, uniformly frustrated with one-half flux quantum per loop and one-half Cooper pair per island. This structure emulates a noise-resistant spin-1/2 system in a vanishing magnetic field. The flux frustration boosts quantum fluctuations and relieves the constraints on junction fabrication. Variability of manipulation and optimized readout are additional benefits of this design.     

Order parameter quantum fluctuations in a two-dimensional system of mesoscopic Josephson junctions

The boson lattice Hubbard model is used to study the role of quantum fluctuations of the phase and local density of the superfluid component in establishing a global superconducting state for a system of mesoscopic Josephson junctions or grains. The quantum Monte Carlo method is used to calculate the density of the superfluid component and fluctuations in the number of particles at sites of the two-dimensional lattice for various average site occupation numbers n ₀ (i.e., number of Cooper pairs per grain). For a system of strongly interacting bosons, the phase boundary of the ordered superconducting state lies above the corresponding boundary for its quasiclassical limit—the quantum XY-model—and approaches the latter as n ₀ increases. When the boson interaction is weak in the boson Hubbard model (i.e., the quantum fluctuations of the phase are small), the relative fluctuations of the order parameter modulus are significant when n ₀<10, while quantum fluctuations in the phase are significant when n ₀<8; this determines the region of mesoscopic behavior of the system. Comparison of the results of numerical modeling with theoretical calculations show that mean-field theory yields a qualitatively correct estimate of the difference between the phase diagrams of the quantum XY-model and the Hubbard model. For a quantitative estimate of this difference the free energy and thermodynamic averages of the Hubbard model are expanded in powers of 1/n ₀ using the method of functional integration. Zh. éksp. Teor. Fiz. 113, 261–277 (January 1998)     

Shot noise for resonant Cooper pair tunneling

We study intrinsic noise of current in a superconducting single-electron transistor, taking into account both coherence effects and Coulomb interaction near a Cooper pair resonance. Because of this interplay, the statistics of tunneling events deviates from the Poisson distribution and, more important, it shows even-odd asymmetry in the transmitted charge. The zero-frequency noise is suppressed significantly when the quasiparticle tunneling rates are comparable to the coherent oscillation frequency of Cooper pairs.     

Quantum fluctuations in a scale-free network-connected Ising system

We study the effect of quantum fluctuations in an Ising spin system on a scale-free network of degree exponent γ>5 using a quantum Monte Carlo simulation technique. In our model, one can adjust the magnitude of the magnetic field perpendicular to the Ising spin direction and can therefore control the strength of quantum fluctuations for each spin. Our numerical analysis shows that quantum fluctuations reduce the transition temperature T_c of the ferromagnetic-paramagnetic phase transition. However, the phase transition belongs to the same mean-field type universality class both with and without the quantum fluctuations. We also study the role of hubs by turning on the quantum fluctuations exclusively at the nodes with the most links. When only a small number of hub spins fluctuate quantum mechanically, T_c decreases with increasing magnetic field until it saturates at high fields. This effect becomes stronger as the number of hub spins increases. In contrast, quantum fluctuations at the same number of “non-hub” spins do not affect T_c. This implies that the hubs play an important role in maintaining order in the whole network.     

Mechanical Cooper pair transportation as a source of long-distance superconducting phase coherence

Transportation of Cooper pairs by a movable single Cooper-pair box placed between two remote superconductors is shown to establish coherent coupling between them. This coupling is due to entanglement of the movable box with the leads and is manifested in the suppression of quantum fluctuations of the relative phase of the order parameters of the leads. It can be probed by attaching a high resistance Josephson junction between the leads and measuring the current through this junction. The current is suppressed with increasing temperature.     

Charge oscillations in superconducting nanodevices coupled to external environments

Charge oscillations in certain nanodevices, more specifically the so-called Superconducting Cooper Pair Boxes (SCB), are usually interpreted as an effect of macroscopic quantum coherence; an alternative explanation is however possible in terms of the Gross-Pitaevski equation for the classical order parameter. These two explanations are based on different quantum states assigned to the SCB, occupation number states in the first case, coherent-like states in the second one. We show that, when the SCB is weakly coupled to an external source of noise and dissipation, occupation number states are much more unstable than coherent ones.     

Josephson array of mesoscopic objects. Modulation of system properties through the chemical potential

The phase diagram of a two-dimensional Josephson array of mesoscopic objects (superconducting granules, superfluid helium in a porous medium, traps with Bose-condensed atoms, etc.) is examined. Quantum fluctuations in both the modulus and phase of the superconducting order parameter are taken into account within a lattice boson Hubbard model. Modulating the average occupation number n ₀ of the sites in the system (the “number of Cooper pairs” per granule, the number of atoms in a trap, etc.) leads to changes in the state of the array, and the character of these changes depends significantly on the region of the phase diagram being examined. In the region where there are large quantum fluctuations in the phase of the superconducting order parameter, variation of the chemical potential causes oscillations with alternating superconducting (superfluid) and normal states of the array. On the other hand, in the region where the bosons interact weakly, the properties of the system depend monotonically on n ₀. Lowering the temperature and increasing the particle interaction force lead to a reduction in the width of the region of variation in n ₀ within which the system properties depend weakly on the average occupation number. The phase diagram of the array is obtained by mapping this quantum system onto a classical two-dimensional XY model with a renormalized Josephson coupling constant and is consistent with our quantum path-integral Monte Carlo calculations. Zh. éksp. Teor. Fiz. 114, 591–604 (August 1998)     

Finite-bias Cooper pair splitting

In a device with a superconductor coupled to two parallel quantum dots (QDs) the electrical tunability of the QD levels can be used to exploit nonclassical current correlations due to the splitting of Cooper pairs. We experimentally investigate the effect of a finite potential difference across one quantum dot on the conductance through the other completely grounded QD in a Cooper pair splitter fabricated on an InAs nanowire. We demonstrate that the nonlocal electrical transport through the device can be tuned by electrical means and that the energy dependence of the effective density of states in the QDs is relevant for the rates of Cooper pair splitting (CPS) and elastic cotunneling. Such experimental tools are necessary to understand and develop CPS-based sources of entangled electrons in solid-state devices.     

Fluctuation instability of the Dirac Sea in quark models of strong interactions

A number of exactly integrable (quark) models of quantum field theory that feature an infinite correlation length are considered. An instability of the standard vacuum quark ensemble, a Dirac sea (in spacetimes of dimension higher than three), is highlighted. It is due to a strong ground-state degeneracy, which, in turn, stems from a special character of the energy distribution. In the case where the momentumcutoff parameter tends to infinity, this distribution becomes infinitely narrow and leads to large (unlimited) fluctuations. A comparison of the results for various vacuum ensembles, including a Dirac sea, a neutral ensemble, a color superconductor, and a Bardeen–Cooper–Schrieffer (BCS) state, was performed. In the presence of color quark interaction, a BCS state is unambiguously chosen as the ground state of the quark ensemble.     

Readout of superconducting flux qubit state with a Cooper pair box

We study a readout scheme of a superconducting flux qubit state with a Cooper pair box as a transmon. The qubit states consist of the superpositions of two degenerate states where the charge and phase degrees of freedom are entangled. Owing to the robustness of the transmon against external fluctuations, our readout scheme enables the quantum non-demolition and single-shot measurement of flux qubit states. The qubit state readout can be performed by using the nonlinear Josephson amplifiers after a π/2 rotation driven by an ac electric field.     

Reducing the linewidth of an atom laser by feedback

A continuous atom laser will almost certainly have a linewidth dominated by the effect of the atomic interaction energy, which turns fluctuations in the condensate atom number into fluctuations in the condensate frequency. These correlated fluctuations mean that information about the atom number could be used to reduce the frequency fluctuations, by controlling a spatially uniform potential. We show that feedback based on a physically reasonable quantum nondemolition measurement of the atom number of the condensate in situ can reduce the linewidth enormously.