Quasiparticle Beam Research Articles

Andreev reflection in rotating superfluid 3He-B

Andreev reflection of quasiparticle excitations from quantized line vortices is reviewed in the isotropic B phase of superfluid 3He in the temperature regime of ballistic quasiparticle transport at T ≤ 0.20T c . The reflection from an array of rectilinear vortices in solid-body rotation is measured with a quasiparticle beam illuminating the array mainly in the orientation along the rotation axis. The result is in agreement with the calculated Andreev reflection. The Andreev signal is also used to analyze the spin-down of the superfluid component after a sudden impulsive stop of rotation from an equilibrium vortex state. In a measuring setup where the rotating cylinder has a rough bottom surface, annihilation of the vortices proceeds via a leading rapid turbulent burst followed by a trailing slow laminar decay, from which the mutual friction dissipation can be determined. In contrast to the currently accepted theory, it is found to have a finite value in the zero-temperature limit: α(T→0) = (5 ± 0.5) × 10−4.

A Quasiparticle Detector for Imaging Quantum Turbulence in Superfluid $$^3$$ 3 He-B

We describe the development of a two-dimensional quasiparticle detector for use in visualising quantum turbulence in superfluid $$^3$$ He-B at ultra-low temperatures. The detector consists of a $$5 \times 5$$ matrix of pixels, each a 1 mm diameter hole in a copper block containing a miniature quartz tuning fork. The damping on each fork provides a measure of the local quasiparticle flux. The detector is illuminated by a beam of ballistic quasiparticles generated from a nearby black-body radiator. A comparison of the damping on the different forks provides a measure of the cross-sectional profile of the beam. Further, we generate a tangle of vortices (quantum turbulence) in the path of the beam using a vibrating wire resonator. The vortices cast a shadow onto the face of the detector due to the Andreev reflection of quasiparticles in the beam. This allows us to image the vortices and to investigate their dynamics. Here we give details of the design and construction of the detector and show some preliminary results for one row of pixels which demonstrates its successful application to measuring quasiparticle beams and quantum turbulence.

Wave kinetics and photon acceleration

We review recent theoretical work on photon kinetics and wave kinetics in a plasma, where resonant interactions of waves with photons, and with quasi-particles such as plasmons, is considered. A Wigner function, or quasi-distribution function, for photons and quasi-particles, is introduced. The resulting wave kinetic equation is able to describe the evolution of a broad photon spectrum, or more generally, a turbulent plasma state, if conveniently coupled with the wave equations via ponderomotive force terms. Resonant interactions occur when the phase velocity of the large scale wave (for instance a wakefield) is equal to the group velocity of the short wavelength quasi-particles (for instance a short laser pulse). It is shown that quasi-particle Landau damping can take place, as well as quasi-particle beam instabilities. A direct link between short and large wavelength perturbations in the plasma is established. Photon and quasi-particle acceleration and trapping is also discussed.

Vortex Generation in Superfluid3He by a Vibrating Grid

Recently we have found that a vibrating wire resonator produces turbulence in superfluid 3He-B at low temperatures when driven above its pair-breaking critical velocity. The vorticity is produced along with a beam of excitations from pair breaking. Here, we discuss preliminary measurements of turbulence generated from an oscillating grid at low temperatures. The grid oscillator is made from a goal-post shaped vibrating wire resonator supporting a fine copper mesh. While the dissipation by a conventional wire resonator is dominated by pair-breaking at the velocities required for turbulence generation, the dissipation of the grid oscillator appears to be dominated by turbulence. This allows us to generate turbulence without the unwanted effects of a quasiparticle beam. Preliminary measurements suggest that the grid turbulence has a rather different behaviour from that generated by conventional wire resonators.

Fractionally charged quasiparticles

Fractionally charged quasiparticles were proposed by Laughlin to explain the fractional quantum Hall effect. Flowing in one-dimensional-like strips along the edges of the sample the quasiparticles are expected to condense to a chiral Luttinger liquid (CLL). Adding a backscattering impurity in the path of the quasiparticles induces correlation among the scattering events at sufficiently low temperatures, hence leading to highly non-linear I–V characteristic and non-Poissonian shot noise. Moreover, a sufficiently strong backscatterer induces bunching of the backscattered quasiparticles with a super Poissonian shot noise corresponding to stochastic transfer of electrons. Diluting the impinging quasiparticle beam mimics an increased temperature. For example, correlation among scattering events in dilute beams relaxes and bunching ceased altogether. At finite temperature and fractionally charged quasiparticles are found to traverse almost opaque barriers. Turning to the extremely low-temperature regime ( ∼9 mK ) we found unexpected results. At higher order fractions, ν= p/ m with p>1, and very weak backscattering potential a spontaneous bunching of quasiparticles to q= νe took place, namely, at ν=2/5, q=2 e/5 and at ν=3/7, q∼3 e/7. As the temperature increases bunching ceased and the scattered charge was again the familiar Laughlin's quasiparticle q= e/ m independent of p.

Resonant quasiparticles in plasma turbulence.

A general view is proposed on wave propagation in fluids and plasmas where the resonant interaction of monochromatic waves with quasiparticles is considered. A kinetic equation for quasiparticles is used to describe the broadband turbulence interacting with monochromatic waves. Resonant interactions occur when the phase velocity of the long wavelength monochromatic wave is nearly equal to the group velocity of short wavelength wave packets, or quasiparticles, associated with the turbulent spectrum. It is shown that quasiparticle Landau damping can take place, as well as quasiparticle beam instabilities, thus establishing a direct link between short and large wavelength perturbations of the medium. This link is distinct from the usual picture of direct and inverse energy cascades, and it can be used as a different paradigm for the fluid and plasma turbulence theories.

Anomalous chiral Luttinger liquid behavior of diluted fractionally charged quasiparticles

Fractionally charged quasiparticles in edge states, are expected to condense to a chiral Luttinger liquid (CLL). We studied their condensation by measuring the conductance and shot noise due to an artificial backscatterer embedded in their path. At sufficiently low-temperatures backscattering events were found to be strongly correlated, producing a highly nonlinear current-voltage characteristic and a nonclassical shot noise---both are expected in a CLL. When, however, the impinging beam of quasiparticles was made dilute, either artificially via an additional weak backscatterer or by increasing the temperature, the resultant outgoing noise was classical, indicating the scattering of independent quasiparticles. Here, we study in some detail this surprising crossover from correlated particle behavior to an independent behavior, as a function of beam dilution and temperature.

Spatial extent of quantum turbulence in non-rotating superfluid [formula omitted]He–B

Quantum turbulence has been shown to reflect a beam of quasiparticles in the B-phase of superfluid 3 He by Andreev processes. We have investigated the evolution of the turbulence generated by a vibrating wire resonator driven at high velocities and temperatures down to ∼0.1 T c. The vibrating wire produces vorticity together with the expected quasiparticle beam whenever the wire velocity exceeds the critical pair breaking velocity. By using an array of detector wires we are able to investigate the development of the turbulence both in space and time. We observe that the turbulence propagates preferentially along the direction of the quasiparticle beam and drops off in a roughly exponential manner with a decay length of the order of 2 mm .

Direct observation of the Andreev reflection of a quasiparticle beam by quantum turbulence in superfluid [formula omitted]-B

A beam of quasiparticles from a black-body radiator is directed at a localized region of quantum turbulence generated by a vibrating wire resonator driven at super-critical velocity. We are able to measure directly the fraction of the incident quasiparticle beam which is retro-reflected from the turbulence by Andreev processes. Combining these measurements with previous measurements on the spatial extent of the turbulence may allow us to infer the vortex line density.

Shot noise and the transmission of dilute Laughlin quasiparticles

We analyze theoretically a three-terminal geometry in a fractional quantum Hall system---studied in a recent experiment---which allows a dilute beam of Laughlin quasiparticles to be prepared and subsequently scattered by a point contact. Employing a chiral Luttinger liquid description of the ${\ensuremath{\nu}}^{\ensuremath{-}1}=m$ integer edge states, we compute the current and noise of the quasiparticle beam after transmission through the point contact at finite temperature and bias voltage. A refermionization procedure at $m=2$ allows the current and noise to be computed nonperturbatively for arbitrary transparency of the point contact. Surprisingly, we find that for weak backscattering the zero-temperature limit is subtle and singular even at fixed finite bias voltage. In particular, at $T=0$ the incident charge-$e/m$ quasiparticles are either reflected or else Andreev scattered [backscattering a charge-$(\ensuremath{-}1+1/m)e$ quasihole and transmitting an electron]---Laughlin quasiparticles are not transmitted in this limit. A direct signature of these Andreev processes should be accessible in a particular cross-correlation noise measurement that we propose.

Bunching of fractionally charged quasiparticles tunnelling through high-potential barriers.

Shot noise measurements have been used to measure the charge of quasiparticles in the fractional quantum Hall (FQH) regime. To induce shot noise in an otherwise noiseless current of quasiparticles, a barrier is placed in its path to cause weak backscattering. The measured shot noise is proportional to the charge of the quasiparticles; for example, at filling factor v=1/3, noise corresponding to q=e/3 appears. For increasingly opaque barriers, the measured charge increases monotonically, approaching q=e asymptotically. It was therefore believed that only electrons, or alternatively, three bunched quasiparticles, can tunnel through high-potential barriers encountered by a noiseless current of quasiparticles. Here we investigate the interaction of e/3 quasiparticles with a strong barrier in FQH samples and find that bunching of quasiparticles in the strong backscattering limit depends on the average dilution of the quasiparticle current. For a very dilute current, bunching ceases altogether and the transferred charge approaches q=e/3. This surprising result demonstrates that quasiparticles can tunnel individually through high-potential barriers originally thought to be opaque for them.

Preliminary Measurements of Andreev Reflection of Quasiparticles by Turbulence in Superfluid 3He

We present preliminary measurements of Andreev scattering of quasiparticles from turbulence in the B-phase of superfluid 3 He-B. The turbulence is generated by a vibrating wire resonator driven above its pair-breaking critical velocity. The vortices intercept a beam of quasiparticles generated by a nearby black-body radiator. A substantial fraction of the incident quasiparticles are retro-reflected back into the radiator by Andreev scattering processes. The resulting temperature rise within the radiator provides a direct measurement of the flux of quasiparticles Andreev reflected. The technique provides a sensitive probe of superfluid turbulence in the ultra-low temperature regime.

Andreev Reflection of Quasiparticles by a Vortex Tangle in Superfluid 3He-B?

We have made the surprising discovery that the thermal damping of a vibrating wire resonator in superfluid He-3-B at ultra low temperatures is considerably depressed when a second wire in the vicinity is driven supercritically. The damping of a vibrating wire resonator at low velocities in the B-phase arises from the scattering of quasiparticle excitations and has a temperature dependence proportional to the Boltzmann factor exp(-Delta /kT) at low temperatures. At higher velocities (v > v(L)/3), the wire breaks Cooper pairs and emits a quasiparticle beam. At first sight it seems paradoxical that heating the superfluid can reduce the quasiparticle flux: on a neighbouring wire. We can only understand this on the basis that vorticity emitted by the supercritical wire shields, via Andreev reflection, part of the background quasiparticle flux: from reaching the other wire. If this interpretation, is correct, these techniques will provide a sensitive probe of vortex dynamics in the ultra low temperature regime.

Direct Observation of Quantum Andreev Reflection at Free Surface of SuperfluidH3e

The quantum Andreev reflection has been observed for the first time at the free surface of superfluid ${}^{3}\mathrm{He}\ensuremath{-}B$ in the ballistic temperature region by use of a blackbody radiator with an orifice of 0.2 mm in diameter and 1 mm in length. A quasiparticle beam is produced so as to hit the surface at a small angle of 20\ifmmode^\circ\else\textdegree\fi{} where the normal reflection component does not come back to the detector. The observed reflection rate can be explained by a quasiclassical theory combined with the diffuse scattering of the retroreflected particles at the orifice.

Andreev reflection at free surface of superfluid3He

Quasiparticle reflection at the free surface of superfluid3He-B has been investigated in the ballistic temperature region by use of a blackbody radiator with an orifice of 0.2 mm in diameter and 1 mm long. In order to cut off the normal reflection and to increase Andreev reflection rate, a quasiparticle beam is produced to hit the surface at small angle of 20 degree. The observed Andreev reflection seems to be smaller than that expected from the theory.

Quasiparticle beams in superfluid 3He-B at very low temperatures

We have been interested in developing source-experiment-detector type quasiparticle beam experiments in superfluid 3He for some time. Recently we have developed a new source and detector based on the quasiparticle equivalent of the blackbody radiator. We have already used these devices for a few simple experiments but many more are possible, for example the direct observation of quasiparticle transmission across an A-B interface. The radiators are so sensitive that we can easily see the heat leak entering the liquid from the epoxy walls and also note that the leak from copper walls is more than 100 times smaller than from the epoxy.

Ballistic quasiparticle beam experiments in superfluid3He-B

In3He-B at temperatures of the order of 0.1Tc, where the meanfree path of the excitations measures several hundreds of metres, we are able to perform experiments on fully ballistic quasiparticle beams. We describe the first direct production and detection of a quasiparticle beam in superfluid3He with the use of a black-body radiator. The radiator may be used as a smoothly controllable continuous source and also as a bolometric detector, sensitive to a quasiparticle energy flux of order 100 fW mm−2.

Blackbody source and detector of ballistic quasiparticles in 3He-B: Emission angle from a wire moving at supercritical velocity.

Using a new quasiparticle detector and source consisting of a blackbody radiator, we have made the first measurements of the divergence of a beam of quasiparticles produced by a vibrating-wire resonator moving at supercritical velocities in superfluid $^{3}\mathit{B}$ at the zero-temperature limit. At velocities just above the critical velocity of \ensuremath{\Delta}/3${\mathit{p}}_{\mathit{F}}$ we see a very narrow beam directed along the direction of motion of the wire. As the maximum wire velocity increases the beam spreads to saturate at a half-angle divergence of approximately 55\ifmmode^\circ\else\textdegree\fi{} at a maximum velocity of order \ensuremath{\Delta}/${\mathit{p}}_{\mathit{F}}$.

Quasiparticle Beams with Branch Imbalance in Superfluid 3He

Within a simple model (a moving impurity) we study the possibility of creating a beam of quasiparticles in superfluid 3He–B with an unequal number of particle-like and hole-like excitations (branch imbalance). We calculate the dependence of the number and type of the emitted quasiparticles on the direction and the energy. We find branch imbalance, predominantly in the forward and backward directions, which is strongly energy dependent.

The Ballistics of Quasiparticles in 3He-B at Very Low Temperatures

At temperatures below about Tc/4, the mean free paths of quasiparticles in superfluid 3He-B become extremely long. In consequence the quasiparticles behave entirely ballistically, making possible a number of simple but important experiments:(i) The damping of a vibrating wire measures the momentum density of the quasiparticles which is dominated by the exp (-Δ/kT) gap Boltzmann factor. The damping may be used as a direct 3He thermometer to measure a number of properties including, for example, the effective thermal conductance across a liquid to solid interface. This conductance also reflects the gap Boltzmann factor.(ii) A solid object can move through the liquid at low velocities without dissipation, but above a critical velocity produces quasiparticles by pair-breaking of the condensate seen as a sudden onset of damping.(iii) A supercritically-driven wire resonator thus acts as a quasiparticle source. The ballistic propagation of the quasiparticles can be detected on a distant (∼ mm) wire used as a quasiparticle-wind detector. The mechanical force on the detector wire leads to a small movement of the wire which can be measured with a SQUID.Our observation of this quasiparticle wind yields direct information about the mean free paths and velocities of the excitations and also on the mechanism of the pair-breaking process. These quasiparticle beam methods open up a wide range of possible scattering experiments.