Quantum Phase Fluctuations Research Articles

Fluctuations, size effects, and superconductivity in the CuO2 bilayer.

Recently, several experimental groups have found superconducting behavior of one-unit-cell (i.e., one ${\mathrm{CuO}}_{2}$ bilayer) thick ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7}$ films. Using the functional-integral method, we calculate the critical temperature ${\mathit{T}}_{\mathit{c}}$ for a system of two ${\mathrm{CuO}}_{2}$ planes coupled via a tunneling matrix element that results in Josephson-type coupling. The Coulomb interaction between the two planes is considered via inclusion of quantum phase fluctuations. We take into account the fluctuations of the modulus of the superconducting order parameter in the planes and the fluctuations of the phase difference of the order parameter between the planes. While for samples of infinite size ${\mathit{T}}_{\mathit{c}}$ is strictly zero, samples of finite size L yield an effective two-dimensional to zero-dimensional transition at a finite temperature ${\mathit{T}}_{\mathit{c}}^{\mathrm{*}}$, characterized by a jump in the specific heat. We obtain ${\mathit{T}}_{\mathit{c}}^{\mathrm{*}}$ as a function of L, Josephson coupling parameter, and Coulomb interaction strength and predict the temperature dependence of the specific heat near ${\mathit{T}}_{\mathit{c}}^{\mathrm{*}}$. Our results are consistent with the ${\mathit{T}}_{\mathit{c}}^{\mathrm{*}}$ values observed on the single ${\mathrm{CuO}}_{2}$ bilayer.

Suppression of the Josephson current by quantum phase fluctuations: beyond the adiabatic approximation

We study how the Josephson current in a shunted junction is suppressed when the energy gap Δ is not large compared to the charging energy E C . Then the time dependence of the nonlocal kernels in the effective action describing the junction becomes important. For low ratios of the Josephson energy to E C , the Josephson current deviates by tens of percent from what one obtains in the adiabatic limit (i.e. Δ ≫ E c ).

STUDY ON THE MOST PROBABLE DISTRIBUTION FOR LAUGHLIN WAVE FUNCTIONS

We show that, up to a global phase freedom, the most probable distribution of electrons given by the maxima of modulus square of Laughlin wave function (LWF), which is known to be a wave function for an incompressible liquid state of fractional Hall effect, has a triangular lattice structure. We introduce the Gaussian approximation for the modulus square of LWF. We find that the radial distribution function calculated from the Gaussian approximation has a form close to that of LWF at ν = 1, 1/3 and close to a crystal-like behavior when ν becomes smaller. We interprete the underlying physics to be that in the incompressible liquid regime, the "hidden" triangular lattice is smeared away by the quantum phase fluctuation, and as a precursor for liquid-crystal transition when the filling ν decreases towards the crystallization regime, it might manifest itself to be a sort of correlated short-range ordered density fluctuation.

Collapses and revivals of phase fluctuations in parametric down-conversion with quantum pump

The long-time behaviour of the phase quantum fluctuations in the field produced by the parametric down-conversion with a quantum pump is studied. It is shown that if the pump is initially in a coherent state the phase variances for both the signal and the pump modes show collapses and revivals in their long-time evolution.

Quantum phase fluctuations in the Jaynes-Cummings model: effects of cavity damping

Phase properties of a coherent field interacting with a two-level atom in a cavity with very high but finite Q are studied. It is shown that due to the cavity damping the field phase is randomized more quickly than in the ideal-lossless-cavity case. The Hermitian phase distribution and the phase distributions associated with the Q function and the Wigner function are compared. The similarities between them have a clear interpretation in terms of the area of overlap in phase space.

Phase properties of quantum states of light.

We introduce a phase-space description of quantum phase fluctuations. This description involves the quantum state of light and a reference detector state. It is shown that, if the detector state is the electromagnetic vacuum, this phase-space description is equivalent to Glauber's Q quasidistribution. We investigate phase fluctuations of a weak coherent state and of a squeezed vacuum. We compare our results with the theory of phase fluctuations based on a unitary and nonunitary phase operators

Number and phase quantum fluctuations in the down-conversion with a quantum pump

The photon number and phase quantum fluctuations in the field produced by the down-conversion process with a quantum pump are studied. The fully quantum approach using the method of numerical diagonalization of the interaction Hamiltonian is applied to find the evolution of the system. The evolution of the photon number fluctuations, the joint number of photons probability distribution, the quadrature variances, the joint phase probability distribution, the marginal number and phase distributions for the signal mode, the number and phase uncertainty products and squeezing parameters are calculated and illustrated graphically. The results for the signal mode are compared to the corresponding results for the ideal squeezed vacuum to show the range of validity of the parametric approximation.

Number and phase quantum fluctuations in second harmonic generation

Photon number and phase fluctuations and correlations in the second harmonic generation are discussed. The new Pegg-Barnett Hermitian phase formalism is used to deal with the phase properties of the field. The method of numerical diagonalization of the interaction Hamiltonian is applied to find the state evolution and, consequently, the number and phase quantum fluctuations. It is shown that the joint phase probability distribution evolves into a multi-peak structure indicating clearly the transition from the second harmonic to the down-conversion regime, and back. The evolution of all relevant quantities is illustrated graphically, and their dependence on the mean number of photons of the initial field is shown explicitly. The number-phase uncertainty product for the fundamental mode is plotted making evident the abrupt transition from the low to the high level of quantum fluctuations.

Quantum phase fluctuations in the second-harmonic generation

Quantum phase fluctuations in the second-harmonic generation are examined from the point of view of the Hermitian phase formalism introduced by Pegg and Barnett. The joint probability distribution as well as the variances for the phases of the fundamental and second-harmonic modes are calculated numerically. Their evolution is illustrated graphically, and the phase properties of the generated light are discussed.

Quantum phase fluctuations in parametric down-conversion with quantum pump

The effect of quantum fluctuations of the pump on the quantum phase properties of the signal mode in the parametric down-conversion process is considered. The Pegg-Barnett hermitian phase formalism is used to calculate the joint phase probability distribution and the phase variances of the two modes. The time evolution of the field state is obtained by means of numerical diagonalization of the interaction hamiltonian. The results are illustrated graphically and compared to those for the ideal squeezed state.

Effects of charging-energy fluctuations on an anomalous behavior of mesoscopic Josephson junctions

A theory is proposed for mesoscopic Josephson junctions in the low-temperature intermediate quantum regime in which such junctions are characterized by a large single-electron charging energy {ital E}{sub {ital c}} that is of the order of the Josephson energy, {ital E}{sub {ital J}}. This contrasts with the classical Josephson junctions where the Josephson energy {ital E}{sub {ital J}} is usually dominant. In this intermediate regime the phase difference of the order parameters for left and right superconductors is no longer localized. In particular, it is believed that at low temperature the quantum phase fluctuations play a very important role. By employing functional-integral methods to the junction Hamiltonian, the resistive regimes of the mesoscopic Josephson junctions below the critical current are studied. It is shown that the Josephson current acquires a spectral decomposition, characterized by the spectral width {Delta}{sub {omega}}. The relative values of {Delta}{sub {omega}} and the voltage {ital V} are shown to determine the resistive regimes in the junction.

Charge-fluctuation effect on the critical temperature of layered high-Tcsuperconductors

The value of the superconducting critical temperature (${\mathit{T}}_{\mathit{c}}$) of artificially layered superconductors made out of alternating Y-Ba-Cu-O and Pr-Ba-Cu-O layers is calculated as a function of both the number of layers of pure Y-Ba-Cu-O within a unit cell of the superlattice and the thickness of the insulating (Pr-Ba-Cu-O) layer. The calculation is performed within a model of electrostatically coupled two-dimensional (2D) arrays of ultrasmall Josephson junctions. The underlying mechanism is assumed to be the depression of the Beresinskii-Kosterlitz-Thouless transition temperature (${\mathit{T}}_{\mathrm{BKT}}$) by quantum phase fluctuations due to charging effects. The ${\mathit{T}}_{\mathit{c}}$ value of the entire structure can then be tuned by varying the charging energy that depends on the average neighborhood of a typical site in Cu-O planes of Y-Ba-Cu-O layers. Recent experiments on such structures are described very accurately by the model. Furthermore, the ratio (${\mathit{T}}_{\mathit{c}}^{(\mathit{n})}$-${\mathit{T}}_{\mathit{c}}^{(1)}$)/(${\mathit{T}}_{\mathit{c}}^{(2)}$-${\mathit{T}}_{\mathit{c}}^{(1)}$), where ${\mathit{T}}_{\mathit{c}}^{(\mathit{n})}$ is the critical temperature of a thin film made up of n Y-Ba-Cu-O unit cells, is found to be independent of the fitting parameters. This prediction is well confirmed by available experimental data. Furthermore, the model also applies for the series of Bi- and Tl-based cuprates of general formulas ${\mathrm{Bi}}_{2}$${\mathrm{Sr}}_{2}$${\mathrm{Ca}}_{\mathit{n}\mathrm{\ensuremath{-}}1}$${\mathrm{Cu}}_{\mathit{n}}$${\mathrm{O}}_{\mathit{y}}$ and ${\mathrm{Tl}}_{2}$ (1)${\mathrm{Ba}}_{2}$${\mathrm{Ca}}_{\mathit{n}\mathrm{\ensuremath{-}}1}$${\mathrm{Cu}}_{\mathit{n}}$${\mathrm{O}}_{\mathit{y}}$ containing n Cu-O planes per unit cell, for which the observed values of the ratio \ensuremath{\rho}=(${\mathit{T}}_{\mathit{c}}^{(3)}$-${\mathit{T}}_{\mathit{c}}^{(1)}$)/(${\mathit{T}}_{\mathit{c}}^{(2)}$-${\mathit{T}}_{\mathit{c}}^{(1)}$) agree within 10% with the predicted ones.

Reentrant phenomena in superconductivity of ultrathin amorphous bismuth films

Quasi-reentrant phenomena in superconductivity conditioned by the mechanisms of phase coherence in inhomogeneous two-dimensional systems are studied on ultrathin amorphous films of bismuth. The effects are shown to be appreciably dependent on the film structures. For films of nearly island structure (L≲10 A), the effects can be attributed to competition of Josephson and single-particle tunneling of electrons. Thicker films (10 A ≲L≲15 A) are equivalent to the system of Josephson junctions corresponding to the resistively shunted junction model. In this case the quasi-reentrant phenomena are due to the quantum phase fluctuations and macroscopic tunneling. The influence of quantum phase fluctuations is considered (in contrast to the known previous investigations) by involving not only nonmonotone temperature dependences of resistanceR but also nonmonotone dependencesR(I), R(V) andR(H) obtained for the first time for ultrathin films (I being the current,V the voltage applied, andH the perpendicular magnetic field).

Iansiti et al. reply.

The authors reply to the comment that physical interpretations in terms of quantum phase fluctuations offord on the reduced critical current of high resistant, low-capactance Josephson junction is essentially same as offered by the authors. (AIP)

Power spectrum measurement of a modulated semiconductor laser using an interferometric self-homodyne technique: influence of quantum phase noise and field correlation

The amplitude-phase coupling effect introduces important dynamic line broadening in modulated semiconductor laser systems. The theory of a technique allowing measurement of the broadened spectrum using a single laser is presented. The quantum phase fluctuations of the lasing field are shown to be of great importance to the photocurrent spectrum of the mixed fields. Expressions for the photocurrent spectrum, which is shown to measure the optical field modulation power spectrum, are derived. Measurement results illustrating the theory are also presented. >

Effect of quasiparticle tunneling on quantum-phase fluctuations and the onset of superconductivity in granular films.

Recent experiments on the onset of superconductivity in granular films have raised a number of interesting issues regarding the role of quantum fluctuations of the phase variable. We model the granular film as an ordered array of Josephson-coupled grains, and we take into account quasiparticle tunneling via the method of Ambegaokar, Eckern, and Sch\"on. The onset of superconductivity, at T=0, occurs when the value of the normal-state sheet resistance has a critical value of order h/4${e}^{2}$, which is not very sensitive to the capacitance of the grains.

Quantum phase fluctuations and squeezing in degenerate four-wave mixing

We consider the generation of squeezed states in degenerate four-wave mixing, retaining all significant phase-matched terms in the third-order polarization. It is shown that, for output modes combined with appropriate phase shifts, ideal squeezed states are produced when the pump field is treated classically. An approximation scheme is used to investigate the effect of pump-field quantization. We show that for reasonable crystal lengths, the effect of pump-field quantization is insignificant in the region of significant squeezing.

Quantum phase noise and field correlation in single frequency semiconductor laser systems

The influence of quantum phase fluctuations which affect single frequency semiconductor lasers in various coherent detection systems is discussed in terms of photocurrent autocorrelation and spectral density functions. The general treatment given in this paper can be applied in diverse practical cases and points out the problems of phase correlation and phase matching between the two mixed optical beams. In the more general case the photocurrent spectrum is found to be composed of discrete and quasi-Lorentzian parts whose energies and spectral spreads are discussed as a function of the laser line width, the phase matching and the phase correlation between the two coherently combined fields.

Organic superconductors: Magnetism versus superconductivity and the fluctuating regime

Superconductivity which is observed in the series of quasi-one-dimensional organic conductors (TMTSF) 2X is characterized by experimental features which can be related to the strong anisotropy of the band structure of these materials. We shall emphasize the interplay between magnetically ordered and superconducting ground states and the existence of a field-dependent depression of the density of states at the Fermi level below 30 K or so. Finally, we point out briefly that the quasi mean-field behavior of the superconducting transition at 1.2 K in (TMTSF) 2ClO 4 can be easily reconciled with a broad one-dimensional fluctuation regime within the framework of a quasi-one-dimensional theory which takes into account the quantum phase fluctuations of the order parameter and a band structure anisotropy not larger than 10.

On the relevance of quantum phase fluctuations

The long-range fluctuations in the phase of the order parameter are derived for a long thin superconducting specimen using thermodynamic fluctuation theory. Only states with constant phase gradients contribute to the above calculation. The fluctuations are viewed as being of two distinct kinds: (a) fluctuations of the phase difference along a small part of the specimen with a constant overall phase change; (b) fluctuations between (discrete) states with different phase changes over the whole sample. It is argued that the fluctuations of the type (a) are a very short time phenomenon, not related to the destruction of superconductive properties, while the fluctuations (b) relate to and have the same time scale as the decay of metastable currents. The equilibrium superconducting properties are still possible, at given time regimes, in spite of the large phase fluctuations, and without ODLRO.