Thermal Coherence Length Research Articles

Dynamics of thermalization of two tunnel-coupled one-dimensional quasicondensates

We study the non-equilibrium dynamics of two tunnel-coupled one-dimensional quasicondensates following a quench of the coupling strength from zero to a fixed finite value. More specifically, starting from two independent quasicondensates in thermal equilibrium, with initial temperature and chemical potential imbalance, we suddenly switch on the tunnel-coupling and analyze the post-quench equilibration in terms of particle number and energy imbalances. We find that, in certain parameter regimes, the net energy can flow from the colder quasicondensate to the hotter one and is governed by the surplus of low energy particles flowing from the cold to the hot system relative to the high-energy particles flowing in the reverse direction. In all cases, the approach to the new thermal equilibrium occurs through transient, damped oscillations. We also find that for a balanced initial state the coupled quasicondensates can relax into a final thermal equilibrium state in which they display a thermal phase coherence length that is larger than their initial phase coherence length, even though the new equilibrium temperature is higher. The increase in the phase coherence length occurs due to phase locking which manifests itself via an increased degree of correlation between the local relative phases of the quasicondensates at two arbitrary points.

Macroscopic coherence as an emergent property in molecular nanotubes

Nanotubular molecular self-aggregates are characterized by a high degree of symmetry and they are fundamental systems for light-harvesting and energy transport. While coherent effects are thought to be at the basis of their high efficiency, the relationship between structure, coherence and functionality is still an open problem. We analyse natural nanotubes present in Green Sulphur Bacteria. We show that they have the ability to support macroscopic coherent states, i.e. delocalized excitonic states coherently spread over many molecules, even at room temperature. Specifically, assuming a canonical thermal state we find, in natural structures, a large thermal coherence length, of the order of 1000 molecules. By comparing natural structures with other mathematical models, we show that this macroscopic coherence cannot be explained either by the magnitude of the nearest-neighbour coupling between the molecules, which would induce a thermal coherence length of the order of 10 molecules, nor by the presence of long-range interactions between the molecules. Indeed we prove that the existence of macroscopic coherent states is an emergent property of such structures due to the interplay between geometry and cooperativity (superradiance and super-transfer). In order to prove that, we give evidence that the lowest part of the spectrum of natural systems is determined by a cooperatively enhanced coupling (super-transfer) between the eigenstates of modular sub-units of the whole structure. Due to this enhanced coupling strength, the density of states is lowered close to the ground state, thus boosting the thermal coherence length. As a striking consequence of the lower density of states, an energy gap between the excitonic ground state and the first excited state emerges. Such energy gap increases with the length of the nanotube (instead of decreasing as one would expect), up to a critical system size which is close to the length of the natural complexes considered.

Flux-induced Nernst effect in low-dimensional superconductors

A method is available that enables consistent study of the stochastic behavior of a system that obeys purely diffusive evolution equations. This method has been applied to a superconducting loop with nonuniform temperature, with average temperature close to Tc. It is found that a flux-dependent average potential difference arises along the loop, proportional to the temperature gradient and most pronounced in the direction perpendicular to this gradient. The largest voltages were obtained for fluxes close to 0.3Φ0, average temperatures slightly below the critical temperature, thermal coherence length of the order of the perimeter of the ring, BCS coherence length that is not negligible in comparison to the thermal coherence length, and short inelastic scattering time. This effect is entirely due to thermal fluctuations. It differs essentially from the usual Nernst effect in bulk superconductors, that is induced by magnetic field rather than by magnetic flux. We also study the effect of confinement in a 2D mesoscopic film.

Flux-induced Nernst effect in a superconducting loop

When a superconducting ring encloses a magnetic flux that is not an integer multiple of half the quantum of flux, a voltage arises in the direction perpendicular to the temperature gradient. This effect is entirely due to thermal fluctuations. We study the dependence of this voltage on the temperature gradient, flux, position, average temperature, BCS coherence length, thermal coherence length, and the Kramer–Watts-Tobin parameter. The largest voltages were obtained for fluxes close to , average temperatures slightly below the critical temperature, thermal coherence length of the order of the perimeter of the ring and BCS coherence length that is not negligible in comparison to the thermal coherence length. As a rough comparison between the flux-induced and the field-induced effects, we also considered a two-dimensional sample.

Length scales involved in decoherence of trapped bosons by buffer-gas scattering

We ask and answer a basic question about the length scales involved in quantum decoherence: how far apart in space do two parts of a quantum system have to be, before a common quantum environment decoheres them as if they were entirely separate? We frame this question specifically in a cold atom context. How far apart do two populations of bosons have to be, before an environment of thermal atoms of a different species (`buffer gas') responds to their two particle numbers separately? An initial guess for this length scale is the thermal coherence length of the buffer gas; we show that a standard Born-Markov treatment partially supports this guess, but predicts only inverse-square saturation of decoherence rates with distance, and not the much more abrupt Gaussian behavior of the buffer gas's first-order coherence. We confirm this Born-Markov result with a more rigorous theory, based on an exact solution of a two-scatterer scattering problem, which also extends the result beyond weak scattering. Finally, however, we show that when interactions within the buffer gas reservoir are taken into account, an abrupt saturation of the decoherence rate does occur, exponentially on the length scale of the buffer gas's mean free path.

Two-point density correlations of quasicondensates in free expansion

We measure the two-point density correlation function of freely expanding quasicondensates in the weakly interacting quasi-one-dimensional (1D) regime. While initially suppressed in the trap, density fluctuations emerge gradually during expansion as a result of initial phase fluctuations present in the trapped quasicondensate. Asymptotically, they are governed by the thermal coherence length of the system. Our measurements take place in an intermediate regime where density correlations are related to near-field diffraction effects and anomalous correlations play an important role. Comparison with a recent theoretical approach described by Imambekov et al. yields good agreement with our experimental results and shows that density correlations can be used for thermometry of quasicondensates.

Electron–electron interaction induced spin thermalization in quasi-low-dimensional spin valves

We study the spin thermalization, i.e., the inter-spin energy relaxation mediated by electron–electron scattering in small spin valves. When one or two of the dimensions of the spin valve spacer are smaller than the thermal coherence length, the direct spin energy exchange rate diverges and needs to be regularized by the sample dimensions. Here we consider two model systems: a long quasi-1D wire and a thin quasi-2D sheet.

Magnetoresistive oscillations in a doubly connected SFS interferometer with a ferromagnetic segment longer than the thermal coherence length

The conductance of ferromagnetic Ni samples of macroscopic length between F/S interfaces closed by a superconductor indium (an SNS system in the Andreev interferometer geometry) is investigated. The macroscopic size of the system makes it possible to measure directly the conductance of each of the elements of the branched AI circuit and to arrange conditions under which the contribution of side effects, reminiscent of the proximity effect, are minimal. The hc/2e oscillations of the resistance with respect to magnetic field (the Aharonov — Bohm effect in disordered conductors), with an amplitude corresponding to the positive interference contribution to the resistance of an F/S interfacial region with a thickness of the order of the coherence length of the subgap excitations upon Andreev reflection in the presence of an exchange field typical for ferromagnetic materials (∼ 1 nm), are observed for the first time at lengths of the ferromagnetic segments exceeding the typical mesoscopic scale (∼ lμm) by more than a factor of 103.

Magnetoresistive oscillations in a doubly connected SFS interferometer with a ferromagnetic segment longer than the thermal coherence length

The conductance of ferromagnetic Ni samples of macroscopic length between F/S interfaces closed by a superconductor (indium) — an SNS system in the “Andreev interferometer” (AI) geometry — is investigated. The macroscopic size of the system makes it possible to measure directly the conductance of each of the elements of the branched AI circuit and to arrange conditions under which the contribution of “side” effects, reminiscent of the proximity effect, are minimal. The hc∕2e oscillations of the resistance with respect to magnetic field (the Aharonov–Bohm effect in disordered conductors), with an amplitude corresponding to the positive interference contribution to the resistance of an F/S interfacial region with a thickness of the order of the coherence length of the subgap excitations upon Andreev reflection in the presence of an exchange field typical for ferromagnetic materials (∼1nm), are observed for the first time at lengths of the ferromagnetic segments exceeding the typical mesoscopic scale (∼1μm) by more than a factor of 103.

Renormalization group study of the conductances of interacting quantum wire systems with different geometries

We examine the effect of interactions between the electrons on the Landauer-B\"uttiker conductances of some systems of quantum wires with different geometries. The systems include a long wire with a stub in the middle, a long wire containing a ring which can enclose a magnetic flux, and a system of four long wires which are connected in the middle through a fifth wire. Each of the wires is taken to be a weakly interacting Tomonaga-Luttinger liquid, and scattering matrices are introduced at all the junctions present in the systems. Using a renormalization group method developed recently for studying the flow of scattering matrices for interacting systems in one dimension, we compute the conductances of these systems as functions of the temperature and the wire lengths. We present results for all three regimes of interest, namely, high, intermediate, and low temperature. These correspond, respectively, to the thermal coherence length being smaller than, comparable to, and larger than the smallest wire length in the different systems, i.e., the lengths of the stub or each arm of the ring or the fifth wire. The renormalization group procedure and the formulas used to compute the conductances are different in the three regimes. In particular, the dimensionality of the scattering matrix effectively changes when the thermal length becomes larger than the smallest wire length. We also present a phenomenologically motivated formalism for studying the conductances in the intermediate regime where there is only partial coherence. At low temperatures, we study the line shapes of the conductances versus the energy of the electrons near some of the resonances; the widths of the resonances are found to go to zero with decreasing temperature. Our results show that the Landauer-B\"uttiker conductances of various systems of experimental interest depend on the temperature and lengths in a non-trivial way when interactions are taken into account.

Magnetic response of clean NS proximity cylinders

We discuss recent investigations on the magnetic response of NS proximity cylinders of niobium coated with a clean silver layer at 150 μK<T<9 K , which show strong induced superconductivity in N. The temperature dependence of the susceptibility in the diamagnetic regime is described successfully by the quasiclassical Eilenberger theory including an elastic mean free path ℓ as the only fit parameter. In the mesoscopic temperature regime the NS system shows the paramagnetic reentrant effect, superimposing on the full Meissner screening. The logarithmic slope of the reentrant paramagnetic susceptibility χ para( T)∝exp(− L/ ξ N) is limited by the condition ξ N= nL with ξ N=ℏ v F/2π k B T, the thermal coherence length. In AgNb wires with perimeter L=72 μm , we observe the integer multiples n=1,2,4 as T is reduced.

Paramagnetic reentrant effect in high purity mesoscopic AgNb proximity structures

We discuss the magnetic response of clean Ag coated Nb proximity cylinders in the temperature range 150 &mgr;K<T<9 K. In the mesoscopic temperature regime, the normal-metal-superconductor system shows the yet unexplained paramagnetic reentrant effect, discovered some years ago [P. Visani, A. C. Mota, and A. Pollini, Phys. Rev. Lett. 65, 1514 (1990)], superimposing on full Meissner screening. The logarithmic slope of the reentrant paramagnetic susceptibility chi(para)(T) approximately exp(-L/xi(N)) is limited by the condition xi(N) = n L, with xi(N) = Planck's over 2piv(F)/2pik(B)T, the thermal coherence length and n = 1,2,4. At the lowest temperatures, chi(para) compensates the diamagnetic susceptibility of the whole AgNb structure.

Reentrance of the Metallic Conductance in a Mesoscopic Proximity Superconductor.

We present an experimental study of the diffusive transport in a normal metal near a superconducting interface, showing the re-entrance of the metallic conductance at very low temperature. This new mesoscopic regime comes in when the thermal coherence length of the electron pairs exceeds the sample size. This re-entrance is suppressed by a bias voltage given by the Thouless energy and can be strongly enhanced by an Aharonov Bohm flux. Experimental results are well described by the linearized quasiclassical theory.

Experimental S-2DEG-S junction characteristics and a novel interpretation

We present experimental transport characteristics of long and ballistic superconductor - 2-dimensional electron gas - superconductor junctions obtained in a temperature range from 1K down to 10mK. Surprisingly the critical current I-c can be fitted to the ideal junction temperature dependence, I-c(T) proportional to exp(-T/T-0) approximate to exp(-L/xi(T)), with xi(T) the thermal coherence length, despite the presence of interface barriers and a to small I-c. We propose that the conflict between the experimental data and the theoretical predictions for these non ideal junctions might be resolved by employing concepts from the theory of disorder induced opening of tunnel channels.

Optical phase fluctuations thermally induced in a single-mode optical fiber

Mathematical expressions have been derived on fluctuations of optical phase and frequency of a light wave which are thermally caused in a single-mode optical fiber in terms of fiber length, thermal coherence length, and fluctuation frequency. Fluctuations of optical phase and temperature were measured at a wavelength of 0.6328 microm by Mach-Zehnder interferometry, and the results are compared with theoretical predictions. A minimum detectable temperature change through optical phase shift depends on frequency stability of a source laser. It is 10(-5) K with a fractional frequency fluctuation of 10(-9).