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arXiv:1511.03367

Collective properties of quantum matter: from Hawking radiation analogues to quantum Hall effect in graphene

Juan Ramón Muñoz de Nova

Published Nov 11, 2015• 0 citations
arXivHTMLPDF

Abstract

The work is divided in three parts. We devote the first part to the study of analog Hawking radiation in Bose-Einstein condensates. We study numerically the birth of a sonic black hole in an outcoupled Bose-Einstein condensate after relaxing the confinement provided by an optical lattice. We also study possible signatures of spontaneous Hawking radiation. We propose that the violation of CS inequalities is a smoking gun of the presence of the Hawking effect. We compare this criterion with the presence of entaglement, finding that both are equivalent under usual assumptions. Finally, we study a different gravitational analogue: the so-called black-hole laser. The most interesting result is the appearance of a regime of continuous and periodic emission of solitons, providing the most strong analogue with optical lasers. In the second part, we analyze the effect of the introduction of a short Bragg pulse in a thermal cloud. We show that the induced periodic density pattern decays to the equilibrium profile. However, instead of the usual collisional relaxation, the mechanism responsible for the decay is the thermal disorder of the particles, with a characteristic time that only depends on the temperature. We find a very good agreement with actual experimental data. In the last part, we switch to a very different system: the $ν=0$ quantum Hall state of bilayer graphene. After re-deriving the corresponding mean-field phase diagram, we compute the collective modes within the zero Landau level. Among the most remarkable results, we have found that at the boundary between the FLP and the F phases a gapless mode appears resulting from an accidental symmetry that can be regarded as a remanent of a broken $SO(5)$ symmetry. On the other hand, the CAF and PLP phases can present dynamical instabilities. We straightforwardly extend the previous results to monolayer graphene.

DOI
10.48550/arxiv.1511.03367

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The work is divided in three parts. We devote the first part to the study of analog Hawking radiation in Bose-Einstein condensates. We study numerically the birth of a sonic black hole in an outcoupled Bose-Einstein condensate after relaxing the confinement provided by an optical lattice. We also study possible signatures of spontaneous Hawking radiation. We propose that the violation of CS inequalities is a smoking gun of the presence of the Hawking effect. We compare this criterion with the presence of entaglement, finding that both are equivalent under usual assumptions. Finally, we study a different gravitational analogue: the so-called black-hole laser. The most interesting result is the appearance of a regime of continuous and periodic emission of solitons, providing the most strong analogue with optical lasers. In the second part, we analyze the effect of the introduction of a short Bragg pulse in a thermal cloud. We show that the induced periodic density pattern decays to the equilibrium profile. However, instead of the usual collisional relaxation, the mechanism responsible for the decay is the thermal disorder of the particles, with a characteristic time that only depends on the temperature. We find a very good agreement with actual experimental data. In the last part, we switch to a very different system: the ν=0ν=0ν=0 quantum Hall state of bilayer graphene. After re-deriving the corresponding mean-field phase diagram, we compute the collective modes within the zero Landau level. Among the most remarkable results, we have found that at the boundary between the FLP and the F phases a gapless mode appears resulting from an accidental symmetry that can be regarded as a remanent of a broken SO(5)SO(5)SO(5) symmetry. On the other hand, the CAF and PLP phases can present dynamical instabilities. We straightforwardly extend the previous results to monolayer graphene.
The work is divided in three parts. We devote the first part to the study of analog Hawking radiation in Bose-Einstein condensates. We study numerically the birth of a sonic black hole in an outcoupled Bose-Einstein condensate after relaxing the confinement provided by an optical lattice. We also study possible signatures of spontaneous Hawking radiation. We propose that the violation of CS inequalities is a smoking gun of the presence of the Hawking effect. We compare this criterion with the presence of entaglement, finding that both are equivalent under usual assumptions. Finally, we study a different gravitational analogue: the so-called black-hole laser. The most interesting result is the appearance of a regime of continuous and periodic emission of solitons, providing the most strong analogue with optical lasers. In the second part, we analyze the effect of the introduction of a short Bragg pulse in a thermal cloud. We show that the induced periodic density pattern decays to the equilibrium profile. However, instead of the usual collisional relaxation, the mechanism responsible for the decay is the thermal disorder of the particles, with a characteristic time that only depends on the temperature. We find a very good agreement with actual experimental data. In the last part, we switch to a very different system: the ν=0\nu=0ν=0 quantum Hall state of bilayer graphene. After re-deriving the corresponding mean-field phase diagram, we compute the collective modes within the zero Landau level. Among the most remarkable results, we have found that at the boundary between the FLP and the F phases a gapless mode appears resulting from an accidental symmetry that can be regarded as a remanent of a broken SO(5)SO(5)SO(5) symmetry. On the other hand, the CAF and PLP phases can present dynamical instabilities. We straightforwardly extend the previous results to monolayer graphene.
The propagation of fluctuations in the velocity potential of an inviscid, irrotational fluid is governed by a wave equation very similar to that governing the propagation of massless scalar fields in curved spacetime. This similarity allows certain fluid systems to be used as experimentally realisable models for objects that cannot be studied under controlled conditions, such as black holes and ultrarelativitsic rotating stars. The analogy applies only to the propagation of fields in a fixed background, not to the behaviour of the background itself. However, even this limited similarity has excited a great deal of interest from researchers, since it suggests that phenomena such as superradiance and Hawking radiation may have analogues in superfluids. In recent years, experimental advances in the creation and manipulation of Bose-Einstein condensates have provided researchers with very low temperature systems possessing a uniquely simple microscopic theory. Furthermore, under certain long-length-scale approximations, Bose-Einstein condensates can be described as classical irrotational inviscid fluids, and therefore can be treated as analogues of appropriate gravitational systems. We present a comprehensive and detailed critical review of the mean-field theory of Bose-Einstein condensates, the conditions under which Bose-Einstein condensates can be treated as an analogue gravity system, the construction of analogue black holes, and several derivations of Hawking radiation and analogue Hawking radiation. The interdisciplinary nature of analogue gravity means that the relevant results are widely scattered in the literature, and we consider this critical review and discussion of the relevant literature to be a central and noteworthy element of the project. We then analyse in detail a recent derivation of analogue Hawking radiation in Bose-Einstein condensates as a consequence of quantum depletion. We elucidate the methodology and the physical meaning of the results by comparison with the derivations of Hawking radiation considered previously, and discuss possible extensions and improvements. We also present an original investigation of analogue superradiance in simple vortices, with the vortex density profile chosen to mimic a realistic vortex in a Bose-Einstein condensate. We find that superradiant amplification occurs and is likely to be significant, but our long-length-scale approximation is of dubious validity near the scattering point.
Analogue gravity explores how collective excitations in condensed matter systems can reproduce the behavior of fields in curved spacetimes. An important example is the acoustic black holes that can occur for sound in a moving fluid. In these lecture notes, we focus on atomic Bose-Einstein condensates (BECs), quantum fluids that provide an interesting platform for analogue gravity studies thanks to their accurate theoretical description, remarkable experimental control, and ultralow temperatures that allow the quantum nature of sound to emerge. We give a pedagogical introduction to analogue black holes and the theoretical description of BECs and their elementary excitations, which behave as quantum fields in curved spacetimes. We then apply these tools to survey the current understanding of black-hole superradiance and analogue Hawking radiation, including explicit examples and numerical methods.
We consider elongated condensates that cross twice the speed of sound. In the absence of periodic boundary conditions, the phonon spectrum possesses a discrete and finite set of complex frequency modes that induce a laser effect. This effect constitutes a dynamical instability and is due to the fact that the supersonic region acts as a resonant cavity. We numerically compute the complex frequencies and density–density correlation function. We obtain patterns with very specific signatures. In terms of the gravitational analogy, the flows we consider correspond to a pair of black hole and white hole horizons, and the laser effect can be conceived as self-amplified Hawking radiation. This is verified by comparing the outgoing flux at early time with the standard black hole radiation.
As a contribution to a memorial volume, we provide a comprehensive discussion of resonant configurations in analogue gravity, focusing on its implementation in atomic condensates and combining review features with original insights and calculations. In particular, we jointly analyze the analogues of the Andreev and Hawking effects using a microscopic description based on the Bogoliubov approximation. We perform a detailed study of the thermality of the Andreev and Hawking spectra for canonical black-hole solutions, finding that both can be described by a gray-body distribution to a very good approximation. We contemplate several resonant scenarios whose efficiency to enhance anomalous scattering processes is compared to that of non-resonant setups. The presence of quantum signatures in analogue configurations, such as the violation of Cauchy-Schwarz inequalities or entanglement, is analyzed, observing that resonant configurations highly increase the entanglement signal, especially for the Andreev effect. We also discuss how these results have served as inspiration for the rapidly expanding field of quantum information in high-energy colliders. Finally, we study the physics of black-hole lasers as further examples of resonant analogue structures, distinguishing three stages in its time evolution. For short times, we compute the linear and non-linear spectrum for different models. For intermediate times, we generalize the current analysis of the BHL-BCL crossover. For long times, we discuss the emerging concept of spontaneous Floquet state and its potential implications.
We study double-barrier interfaces separating regions of asymptotically subsonic and supersonic flow of Bose-condensed atoms. These setups contain at least one black hole sonic horizon from which the analogue of Hawking radiation should be generated and emitted against the flow in the subsonic region. Multiple coherent scattering by the double-barrier structure strongly modulates the transmission probability of phonons, rendering it very sensitive to their frequency. As a result, resonant tunneling occurs with high probability within a few narrow frequency intervals. This gives rise to highly non-thermal spectra with sharp peaks. We find that these peaks are mostly associated with decaying resonances and only occasionally with dynamical instabilities. Even at achievable non-zero temperatures, the radiation peaks can be dominated by spontaneous emission, i.e. enhanced zero-point fluctuations, and not, as is often the case in analogue models, by stimulated emission.