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Register a new userMutual Interactions of Phonons, Rotons, and Gravity
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We introduce an effective point-particle action for generic particles living in a zero-temperature superfluid. This action describes the motion of the particles in the medium at equilibrium as well as their couplings to sound waves and generic fluid flows. While we place the emphasis on elementary excitations such as phonons and rotons, our formalism applies also to macroscopic objects such as vortex rings and rigid bodies interacting with long-wavelength fluid modes. Within our approach, we reproduce phonon decay and phonon-phonon scattering as predicted using a purely field-theoretic description of phonons. We also correct classic results by Landau and Khalatnikov on roton-phonon scattering. Finally, we discuss how phonons and rotons couple to gravity, and show that the former tend to float while the latter tend to sink but with rather peculiar trajectories. Our formalism can be easily extended to include (general) relativistic effects and couplings to additional matter fields. As such, it can be relevant in contexts as diverse as neutron star physics and light dark matter detection.
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High-resolution neutron resonance spin-echo measurements of superfluid 4He show that the roton energy does not have the same temperature dependence as the inverse lifetime. Diagrammatic analysis attributes this to the interaction of rotons with thermally excited phonons via both four- and three-particle processes, the latter being allowed by the broken gauge symmetry of the Bose condensate. The distinct temperature dependence of the roton energy at low temperatures suggests that the net roton-phonon interaction is repulsive.
We propose a new method to study non-equilibrium dynamics of scalar fields starting from non-Gaussian initial conditions using Keldysh field theory. We use it to study dynamics of phonons coupled to bosonic and fermionic baths, starting from initial Fock states. We find that in one dimension long wavelength phonons coupled to fermionic baths do not thermalize both at low and high bath temperatures. At low temperature, constraints from energy-momentum conservation lead to a narrow bandwidth of particle-hole excitations and the phonons effectively do not feel the effects of this bath. On the other hand, the strong band edge divergence of particle-hole density of states leads to an undamped polariton-like mode of the dressed phonons above the band edge of the particle-hole excitations. These undamped modes contribute to the lack of thermalization of long wavelength phonons at high temperatures. In higher dimensions, these constraints and the divergence of density of states are weakened and leads to thermalization at all wavelengths.
Measurements on cluster states can be used to process quantum information. But errors in cluster states naturally accrue as error-prone inter-particle interactions entangle qubits. We consider one-dimensional cluster states built from controlled phase, Ising, and XY interactions with slow two-qubit error in the interaction strength, consistent with error models of interactions found in a variety of qubit architectures. We focus on measurement protocols designed to implement perfect teleportation wherein quantum information moves across a cluster state intact. Deviations from perfect teleportation offer a proxy for entanglement that can be degraded by two-qubit gate errors. We detail an experimentally viable teleportation fidelity that offers a measure of the impact of error on the cluster state as a whole. Our fidelity calculations show that the error has a distinctly different impact depending on the underlying interaction used for the two-qubit entangling gate. In particular, the Ising and XY interactions can allow perfect teleportation through the cluster state even with large errors, but the controlled phase interaction does not. Nonetheless, we find that teleportation through cluster state chains of size $N$ has a maximum two-qubit error for teleportation along a quantum channel that decreases as $N^{-1/2}$. To allow construction of larger cluster states, we also design lowest-order refocusing pulses for correcting slow errors in the interaction strength. Our work generalizes to higher-dimensional cluster states and sets the stage for experiments to monitor the growth of entanglement in cluster states built from error-prone interactions.
We study the behavior of the mutual information (MI) in various quadratic fermionic chains, with and without pairing terms and both with short- and long-range hoppings. The models considered include the short-range Kitaev model and also cases in which the area law for the entanglement entropy is - logarithmically or non-logarithmically - violated. When the area law is violated at most logarithmically, the MI is a monotonically increasing function of the conformal four-point ratio x, also for the Kitaev model. Where non-logarithmic violations of the area law are present, then non-monotonic features of MI can be observed, with a structure of peaks related to the spatial configuration of Bell pairs, and the four-point ratio x is found to be not sufficient to capture the whole structure of the MI. For the model exhibiting perfect volume law, the MI vanishes identically. For the Kitaev model, when it is gapped or the range of the pairing is large enough, then the results have vanishing MI for small x. A discussion of the comparison with the results obtained by the AdS/CFT correspondence in the strong coupling limit is presented.
We develop a scheme to generate number squeezing in a Bose-Einstein condensate by utilizing interference between two hyperfine levels and nonlinear atomic interactions. We describe the scheme using a multimode quantum field model and find agreement with a simple analytic model in certain regimes. We demonstrate that the scheme gives strong squeezing for realistic choices of parameters and atomic species. The number squeezing can result in noise well below the quantum limit, even if the initial noise on the system is classical and much greater than that of a poisson distribution.
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