Collisionless collective modes in superfluid 3He (original) (raw)
Collective Modes and f-Wave Pairing Interactions in Superfluid He3
Physical Review Letters, 2006
Precision measurements of collective mode frequencies in superfluid 3 He-B are sensitive to quasiparticle and f -wave pairing interactions. Measurements were performed at various pressures using interference of transverse sound in an acoustic cavity. We fit the measured collective mode frequencies, which depend on the strength of f -wave pairing and the Fermi liquid parameter F s 2 , to theoretical predictions and discuss what implications these values have for observing new order parameter collective modes.
Dispersion induced splitting of the collective mode spectrum in A-phase of superfluid 3He
Physics Letters A, 2009
The whole collective mode spectrum in axial and planar phases of superfluid 3 He with dispersion corrections is calculated for the first time. In axial A-phase the degeneracy of clapping modes depends on the direction of the collective mode momentum k with respect to the vector l (mutual orbital moment of Cooper pairs), namely: the mode degeneracy remains the same as in case of zero momentum k for k l only. For any other directions there is a threefold splitting of these modes, which reaches maximum for k⊥l.
Journal of Low Temperature Physics, 2009
The whole collective mode spectrum in axial and planar phases of superfluid 3He with dispersion corrections is calculated for the first time. In axial A-phase the degeneracy of clapping modes depends on the direction of the collective mode momentum k with respect to the vector l (mutual orbital moment of Cooper pairs), namely: the mode degeneracy remains the same as in case of zero momentum k for k‖l only. For any other directions there is a threefold splitting of these modes, which reaches maximum for k ⊥ l. In planar 2D-phase, which exists in the magnetic field (at H>H C ) we find that for clapping modes the degeneracy depends on the direction of the collective mode momentum k with respect to the external magnetic field H, namely: the mode degeneracy remains the same as in case of zero momentum k for k‖H only. For any other directions different from this one (for example, for k ⊥ H) there is twofold splitting of these modes. The obtained results imply that new interesting features can be observed in ultrasound experiments in axial and planar phases: the change of the number of peaks in ultrasound absorption into clapping mode. One peak, observed for these modes by Ling et al. (J. Low Temp. Phys. 78:187, 1990), will split into two peaks in a planar phase and into three peaks in an axial phase under the change of ultrasound direction with respect to the external magnetic field H in a planar phase and with respect to the vector l in an axial phase. In planar phase, some Goldstone modes in the magnetic field become massive (quasi-Goldstone) and have a similar twofold splitting under the change of ultrasound direction with respect to the external magnetic field H. The obtained results as well will be useful under interpretation of the ultrasound experiments in axial and planar phases of superfluid 3He.
Modes of superfluid 3He in the entire hydrodynamic region
Physica B: Condensed Matter, 1990
Dispersion relations for hydrodynamic modes are normally derived in the limit of small damping. This limit covers the entire hydrodynamic region as long as the region conincides with the small damping region (e.g., in 4He-II). This is not the case in superfluid 3He. In this paper the dispersion relations of second sound and sq-mode are generalized throughout the hydrodynamic region. It might have experimental implications for any 3He experiment dealing with frequencies of Hz and higher. They are discussed in detail.
Discovery of an excited pair state in superfluid 3He
Nature Physics, 2008
Order parameter collective modes are the fingerprint of a condensed phase. The spectroscopy of these modes in superfluid 3 He and unconventional superconductors can provide key information on the symmetry of the condensate as well as the microscopic pairing mechanism responsible for the ground state and excitation energies. We report the discovery of a new collective mode in superfluid 3 He-B which we identify as an excited bound state of Cooper pairs. We use interferometry within an acoustic cavity that is very sensitive to changes in the velocity of transverse sound. Our measurements of sound velocity and mode frequency, together with the observation of acoustic birefringence indicate that this new mode is weakly bound with an excitation energy within 1% of the pair-breaking edge of 2∆. Based on the selection rules for coupling of transverse sound to a collective mode in 3 He-B, combined with the observation of acoustic birefringence near the collective mode frequency, we infer that the new mode is most likely a spin-triplet (S = 1), f -wave pair exciton (L = 3) with total angular momentum, J = 4. The existence of a pair exciton with J = 4 suggests an attractive, sub-dominant, f -wave pairing interaction in liquid 3 He.
Low energy dynamics of gapless and quasi-gapless modes of vortices in superfluid 3^33He-B
We discuss the low energy effective dynamics of gapless excitations of the mass vortices of systems similar to the Ginzburg-Landau description of superfluid helium-3 in the bulk B phase. Our approach is to determine the vortex solution by considering a specific ansatz for the order parameter and minimizing the free energy. The conditions on the β i coefficients required for the stability of the various solutions for the order parameter are calculated. By considering the symmetries that are broken by the vortex solutions we are able to generate the moduli fields associated with the low energy excitations of the vortices. Using these fields we determine the effective free energy describing the dynamics of these excitations.
Non-Abelian quasigapless modes localized on mass vortices in superfluid ^{3}He-B
Physical Review D, 2013
Kelvin waves, or Kelvons, have been known for a long time as gapless excitations propagating along superfluid vortices. These modes can be interpreted as the Nambu-Goldstone excitations arising from the spontaneous breaking of the translational symmetry. Recently a different type of gapless excitation localized on strings -the so-called non-Abelian mode -attracted much attention in high-energy physics. We discuss their relevance in condensed matter physics. Non-Abelian rotational quasigapless excitations could appear on the mass vortices in the B phase of the superfluid 3 He, due to the fact that the order parameter in 3 He-B is tensorial. While the U(1) rotational excitations are well established in vortices with asymmetric cores, the non-Abelian rotational excitations belonging to the same family were not considered.
Broken relative symmetry and the hydrodynamics of superfluid 3He
Physica B+C, 1982
Macroscopic condensed systems sometimes break various continuous symmetries in such a way that they remain invariant under the transformations given by certain combinations of these symmetries. This instance, the breaking of a relative symmetry, is discussed in detail. A system of broken relative symmetry is shown to behave as if it broke all the constituent symmetries but lacked the capability to distinguish between them. Each of the three superfluid phases of 'He breaks a relative symmetry not encountered in any other known condensed system. Hence each of them is the only representative in nature of a characteristic hydrodynamic response. These symmetries are specified and the corresponding hydrodynamics discussed. In addition, recent work on 3He dynamics and related problems, especially the peculiar thermodynamic properties of 3He, rotating in equilibrium, are reviewed
Physical Review B, 2004
The signature of superfluidity in bosonic systems is a sound wave-like spectrum of the single particle excitations which in the case of strong interactions is roughly temperature independent. In fermionic systems, where fermion pairing arises as a resonance phenomenon between free fermions and paired fermionic states (examples are: the atomic gases of 6 Li or 40 K controlled by a Feshbach resonance, polaronic systems in the intermediary coupling regime, d-wave hole pairing in the strongly correlated Hubbard system), remnants of such superfluid characteristics are expected to be visible in the normal state. The single particle excitations maintain there a sound wave like structure for wave vectors above a certain qmin(T) where they practically coincide there with the spectrum of the superfluid phase for T < Tc. Upon approaching the transition from above this region in q-space extends down to small momenta, except for a narrow region around q = 0 where such modes change into damped free particle like excitations.
Theory of pair breaking by vibrating macroscopic objects in superfluid 3He
Physica B: Condensed Matter
An intuitive picture of dissipation through pair breaking by macroscopic, vibrating objects in an isotropic superfluid is presented, which predicts a critical velocity for direct quasi-particle emission of v c = v0/(1 + ~), where v 0 is the Landau velocity and a characterizes the superfluid backflow. A new intermediate frequency regime is identified, in which pulsed experiments should reveal a hierarchy of critical velocities and sinusoidally vibrating objects will exhibit a crossover to diffusive behaviour. A model of flow through a channel with a rough surface is analyzed, which yields for the instantaneous dissipation Q-(v-vc) 5 and Q ,~ v 2, at low and high velocities, respectively.
Quantized Vorticity in Superfluid 3He-A: Structure and Dynamics
Lecture Notes in Physics, 2001
Superfluid 3 He-A displays the largest variety in vortex structure among the presently known coherent quantum systems. The experimentally verified information comes mostly from NMR measurements on the rotating fluid, from which the orderparameter texture can often be worked out. The various vortex structures differ in the topology of their order-parameter field, in energy, critical velocity, and in their response to temporal variations in the externally applied flow. They require different experimental conditions for their creation. When the flow is applied in the superfluid state, the structure with the lowest critical velocity is formed. In 3 He-A this leads to the various forms of continuous (or singularity-free) vorticity. Which particular structure is created depends on the externally applied conditions and on the global order-parameter texture.
Nonlinear acoustic effects in superfluid 3He-B
Physica B: Condensed Matter, 1992
We consider the nonlinear interaction of zero sound with the collective modes of the order-parameter in superfluid 3He-B. The approximate particle-hole symmetry of the 3He-Fermi liquid determines selection rules for the linear and nonlinear coupling of zero sound to the collective modes. Starting from the quasiclassical theory of superfluid 3He, we have shown that the coupling strengths have a simple representation in terms of Feynman diagrams. We predict measurable two-phonon absorption and nonlinear-Raman scattering by the J = 2 + (real squashing) modes at low pressures. Recent observations of two-phonon absorption by a group in Helsinki are compared to the theoretical predictions. Two-phonon absorption can be used to determine the dispersion of the J = 2 + modes. 0921-4526/92/$05.00
Energy spectra of superfluid turbulence in ^{3}He
Physical Review B, 2012
In superfluid 3 He-B, turbulence is carried predominantly by the superfluid component. To explore the statistical properties of this quantum turbulence and its differences from the classical counterpart, we adopt the time-honored approach of shell models. Using this approach, we provide numerical simulations of a Sabra shell model that allows us to uncover the nature of the energy spectrum in the relevant hydrodynamic regimes. These results are in qualitative agreement with analytical expressions for the superfluid turbulent energy spectra that were found using a differential approximation for the energy flux.
Collective Modes in a Unitary Fermi Gas across the Superfluid Phase Transition
Physical Review Letters, 2013
We provide a joint theoretical and experimental investigation of the temperature dependence of the collective oscillations of first sound nature exhibited by a highly elongated harmonically trapped Fermi gas at unitarity, including the region below the critical temperature for superfluidity. Differently from the lowest axial breathing mode, the hydrodynamic frequencies of the higher-nodal excitations show a temperature dependence, which is calculated starting from Landau two-fluid theory and using the available experimental knowledge of the equation of state. The experimental results agree with high accuracy with the predictions of theory and provide the first evidence for the temperature dependence of the collective frequencies near the superfluid phase transition.
Quantum oscillations between two weakly coupled reservoirs of superfluid 3He
Nature, 1997
Arguments first proposed over thirty years ago, based on fundamental quantum-mechanical principles, led to the prediction that if macroscopic quantum systems are weakly coupled together, particle currents should oscillate between the two systems. The conditions for these quantum oscillations to occur are that the two systems must both have a well defined quantum phase, phi, and a different average energy
Quantized Vorticity in Superfluid 3He-A
2000
Superfluid 3He-A displays the largest variety in vortex structure among the presently known coherent quantum systems. The experimentally verified information comes mostly from NMR measurements on the rotating fluid, from which the order-parameter texture can often be worked out. The various vortex structures differ in the topology of their order-parameter field, in energy, critical velocity, and in their response to temporal variations in the externally applied flow. They require different experimental conditions for their creation. When the flow is applied in the superfluid state, the structure with the lowest critical velocity is formed. In 3He-A this leads to the various forms of continuous (or singularity-free) vorticity. Which particular structure is created depends on the externally applied conditions and on the global order-parameter texture.
Superfluid phase of 3 He-B near the boundary
Journal of Physics: Conference Series, 2009
Following our analysis of some older and most recent transverse sound experiments in superfluid 3 He-B we have been able to solve one of the long-existing problem of superfluid quantum liquids in confined geometry, namely, answer a question what is the boundary state of 3 He-B. We have devoted specific attention to the differences between transverse sound experiments data from that obtained in longitudinal sound experiments. In our analysis, we have considered several potentially possible explanations of the above experimental data: existence of a new superfluid phase in the vicinity of the boundary; excitation of different branches of squashing mode by longitudinal and transverse sounds and, finally, deformation of the B-phase near the boundary. The last possibility seems to be the most likely explanation implying that the boundary state of 3 He-B is, in fact, the deformed Bphase, as was first suggested by Brusov and Popov about two decades ago for a case of presence of external perturbations such as a magnetic and an electric fields. Our result implies that influence of a wall or, in other words, a confined geometry does not lead to the existence of a new phase near the boundary, as had been suggested many years ago, but, instead, similarly to the case of other external perturbations (such as magnetic, electric fields etc.), the wall deforms the order parameter of the B-phase and this deformation leads to several very important consequences. For example, frequencies of the collective modes in the vicinity of the boundary change by up to about 20 percent.
A strong-coupling theory of superfluid 4{^ 4} 4 He
We propose a new theoretical approach to the excitation spectrum of superfluid 4 He. It is based on the assumption that, in addition to the usual Feynman density fluctuations, there exist localized modes which describe the short range behaviour in the liquid associated with microscopic cores of quantized vortices. We describe in a phenomenological way the hybridization of those two kinds of excitations and we compare the resulting energy spectrum with experimental data, e.g. the structure factor and the cross section for single quasi-particle excitations. We also predict the existence of another type of excitation interpreted as a vortex loop. The energy of this mode agrees both with critical velocity experiments and high energy neutron scattering. In addition we derive a relation between the condensate fraction and the roton energy and we calculate the reduction of the ground-state energy due to the superfluid order.
High Frequency Sound in Superfluid 3He-B
Journal of Low Temperature Physics, 2008
We present measurements of the absolute phase velocity of transverse and longitudinal sound in superfluid 3 He-B at low temperature, extending from the imaginary squashing mode to near pair-breaking. Changes in the transverse phase velocity near pair-breaking have been explained in terms of an order parameter collective mode that arises from f -wave pairing interactions, the so-called J = 4 − mode. Using these measurements, we establish lower bounds on the energy gap in the B-phase. Measurement of attenuation of longitudinal sound at low temperature and energies far above the pair-breaking threshold, are in agreement with the lower bounds set on pair-breaking. Finally, we discuss our estimations for the strength of the fwave pairing interactions and the Fermi liquid parameter, F s 4 .