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arXiv:2103.16619 · Physical Review A

Early-time behavior of quantum subharmonic generation

Yunjin Choi, Boerge Hemmerling, Shan-Wen Tsai, Allen Paine Mills

Published Apr 28, 2021• 2 citations
arXivHTMLPDF

Abstract

A few years ago Avetissian et al. [Phys. Rev. Lett. 113, 023904 (2014); Phys. Rev. A 92, 023820 (2015)] discovered that the exponential growth rate of the stimulated annihilation photons from a singlet positronium Bose-Einstein condensate should be proportional to the square root of the positronium number density, not to the number density itself. In order to elucidate this surprising result obtained via a field-theoretical analysis, we point out that the basic physics involved is the same as that of resonant subharmonic transitions between two quantum oscillators. Using this model, we show that nonlinearities of the type discovered by Avetissian et al. are not unique to positronium and in fact will be encountered in a wide range of systems that can be modeled as nonlinearly coupled quantum oscillators.

DOI
10.1103/physreva.103.043518

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The article "Ultradilute quantum droplets" by Igor Ferrier-Barbut (Physics Today, April 2019, page 46) was really nice to see. It reported on the creation, at last, of real ultradilute liquid droplets and on the tremendous progress that has been made in that area. However, I was disappointed to see no mention or discussion that ultradilute liquid quantum droplets were predicted a long time ago.11. A. Bulgac, Phys. Rev. Lett. 89, 050402 (2002). https://doi.org/10.1103/PhysRevLett.89.050402,22. P. F. Bedaque, A. Bulgac, G. Rupak, Phys. Rev. A. 68, 033606 (2003). https://doi.org/10.1103/PhysRevA.68.033606 That early work was a major source of inspiration for Dmitry Petrov's 2015 paper on the subject,33. D. S. Petrov, Phys. Rev. Lett. 115, 155302 (2015). https://doi.org/10.1103/PhysRevLett.115.155302 at least according to what he told me years ago.In his discussion of mean-field quantum gases, Ferrier-Barbut doesn't note that the Efimov effect, which involves the creation of an infinite number of three-body bound states, can also allow Bose liquids to exist when the scattering length is negative (that is, when the two-particle interaction is attractive). Such a system is not always unstable. Tsung-Dao Lee, Kerson Huang, and Chen Ning Yang (LHY) proposed in 1957 a leading-order correction to the mean-field approximation due to two-body collisions, which was used by Petrov;33. D. S. Petrov, Phys. Rev. Lett. 115, 155302 (2015). https://doi.org/10.1103/PhysRevLett.115.155302 that "game-changing correction," as Ferrier-Barbut calls it, can alter the nature of the Bose–Einstein condensate.However, as was discussed quite some time ago,11. A. Bulgac, Phys. Rev. Lett. 89, 050402 (2002). https://doi.org/10.1103/PhysRevLett.89.050402,22. P. F. Bedaque, A. Bulgac, G. Rupak, Phys. Rev. A. 68, 033606 (2003). https://doi.org/10.1103/PhysRevA.68.033606 the strength of three-body interactions can dominate over LHY corrections and can be infinite even if the two-body scattering length is finite.11. A. Bulgac, Phys. Rev. Lett. 89, 050402 (2002). https://doi.org/10.1103/PhysRevLett.89.050402 A liquid model based on the Efimov effect11. A. Bulgac, Phys. Rev. Lett. 89, 050402 (2002). https://doi.org/10.1103/PhysRevLett.89.050402,22. P. F. Bedaque, A. Bulgac, G. Rupak, Phys. Rev. A. 68, 033606 (2003). https://doi.org/10.1103/PhysRevA.68.033606 is more robust than the one Petrov envisioned and much more flexible than the van der Waals model. Unlike the quantum liquid droplets created in mixtures of Bose–Einstein condensates,44. C. R. Cabrera et al., Science 359, 301 (2018). https://doi.org/10.1126/science.aao5686 which have practically the same size for particle numbers up to tens of thousands, the quantum liquid droplets I suggested are truly saturating systems, with basically constant interior density. A droplet can have any size, and it can be formed even from a single element. It is a real liquid, with constant density inside and a well-defined surface, and its density and surface tension can be controlled. Also, it is stable against quantum corrections to the mean field.22. P. F. Bedaque, A. Bulgac, G. Rupak, Phys. Rev. A. 68, 033606 (2003). https://doi.org/10.1103/PhysRevA.68.033606Moreover, in a rather special system—an ensemble of spin-polarized tritium atoms—three-body recombination processes are most likely absent.22. P. F. Bedaque, A. Bulgac, G. Rupak, Phys. Rev. A. 68, 033606 (2003). https://doi.org/10.1103/PhysRevA.68.033606,55. D. Blume et al., Phys. Rev. Lett. 89, 163402 (2002). https://doi.org/10.1103/PhysRevLett.89.163402 Although I did not make the estimates, which should be straightforward, I am sure that by controlling the density and thus the rate of four-body recombination, one could create droplets with basically arbitrarily long lifetimes. A droplet of spin-polarized tritium atoms would be a totally unique object, perhaps as unique as macroscopic superfluid helium, but amenable to precise quantum many-body calculations, both static and time-dependent. Quantum turbulence could be studied in a large class of systems, for which a microscopic theory exists, and unlike in the case of superfluid helium, theory could be directly confronted with experiment.Quantum liquid droplets could be either boselets or fermilets and would undergo at least two types of phase transitions, from superfluid to normal and from liquid to gas. Their physics should be fascinating. Mixing bosons and fermions can lead to even more interesting and complex objects.ReferencesSection:ChooseTop of pageReferences <<CITING ARTICLES1. A. Bulgac, Phys. Rev. Lett. 89, 050402 (2002). https://doi.org/10.1103/PhysRevLett.89.050402, Google ScholarCrossref2. P. F. Bedaque, A. Bulgac, G. Rupak, Phys. Rev. A. 68, 033606 (2003). https://doi.org/10.1103/PhysRevA.68.033606, Google ScholarCrossref3. D. S. Petrov, Phys. Rev. Lett. 115, 155302 (2015). https://doi.org/10.1103/PhysRevLett.115.155302, Google ScholarCrossref4. C. R. Cabrera et al., Science 359, 301 (2018). https://doi.org/10.1126/science.aao5686, Google ScholarCrossref5. D. Blume et al., Phys. Rev. Lett. 89, 163402 (2002). https://doi.org/10.1103/PhysRevLett.89.163402, Google ScholarCrossref© 2020 American Institute of Physics.

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Parametric instability of a two-component Bose-Einstein condensate driven by a strong time-dependent magnetic field

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We investigate the behavior of a two-component Bose-Einstein condensate (BEC) driven by a strong time-dependent resonant magnetic field. The external resonant field couples two hyperfine states via a one-photon transition. It is shown that a first-order parametric instability of a BEC appears if the local atomic number density exceeds a threshold value that is proportional to the driving field. It is shown that the spatial-dependent increment of instability is proportional to the square of the local atomic density. This instability is determined by the nonlinearity of the BEC associated with the short-range interactions between the atoms.

Physical Review A•Jan 17, 2001•5 citations
A few years ago Avetissian et al. [Phys. Rev. Lett. 113, 023904 (2014); Phys. Rev. A 92, 023820 (2015)] discovered that the exponential growth rate of the stimulated annihilation photons from a singlet positronium Bose-Einstein condensate should be proportional to the square root of the positronium number density, not to the number density itself. In order to elucidate this surprising result obtained via a field-theoretical analysis, we point out that the basic physics involved is the same as that of resonant subharmonic transitions between two quantum oscillators. Using this model, we show that nonlinearities of the type discovered by Avetissian et al. are not unique to positronium and in fact will be encountered in a wide range of systems that can be modeled as nonlinearly coupled quantum oscillators.
We present a numerical study of the dynamical effects following a sudden change of the transverse trapping frequency in an elongated Bose-Einstein condensate, which induces periodic oscillations of the radial density. At early times, we observe an exponential growth of the number of resonant longitudinal phonons, in agreement with the predictions of the Bogoliubov-de Gennes treatment. We then observe an ordered sequence of phenomena induced by the nonlinearities of the Gross-Pitaevskii equation. The first is a loss of the nonseparability of the resonant phonon pairs. This is followed by the saturation of the exponential growth and a strong depletion of condensed atoms. Notably, these effects are well-described by effective 1D dynamics, and are hardly affected by the damping of the radial oscillations. Finally, the atomic spectrum becomes broad, featureless and almost incoherent, in agreement with experimental results obtained in [J.-C. Jaskula et al., Phys. Rev. Lett. 109, 220401 (2012)]. The link between this sequence of events and the preheating scenario in inflationary cosmology is striking.
The article "Ultradilute quantum droplets" by Igor Ferrier-Barbut (Physics Today, April 2019, page 46) was really nice to see. It reported on the creation, at last, of real ultradilute liquid droplets and on the tremendous progress that has been made in that area. However, I was disappointed to see no mention or discussion that ultradilute liquid quantum droplets were predicted a long time ago.11. A. Bulgac, Phys. Rev. Lett. 89, 050402 (2002). https://doi.org/10.1103/PhysRevLett.89.050402,22. P. F. Bedaque, A. Bulgac, G. Rupak, Phys. Rev. A. 68, 033606 (2003). https://doi.org/10.1103/PhysRevA.68.033606 That early work was a major source of inspiration for Dmitry Petrov's 2015 paper on the subject,33. D. S. Petrov, Phys. Rev. Lett. 115, 155302 (2015). https://doi.org/10.1103/PhysRevLett.115.155302 at least according to what he told me years ago.In his discussion of mean-field quantum gases, Ferrier-Barbut doesn't note that the Efimov effect, which involves the creation of an infinite number of three-body bound states, can also allow Bose liquids to exist when the scattering length is negative (that is, when the two-particle interaction is attractive). Such a system is not always unstable. Tsung-Dao Lee, Kerson Huang, and Chen Ning Yang (LHY) proposed in 1957 a leading-order correction to the mean-field approximation due to two-body collisions, which was used by Petrov;33. D. S. Petrov, Phys. Rev. Lett. 115, 155302 (2015). https://doi.org/10.1103/PhysRevLett.115.155302 that "game-changing correction," as Ferrier-Barbut calls it, can alter the nature of the Bose–Einstein condensate.However, as was discussed quite some time ago,11. A. Bulgac, Phys. Rev. Lett. 89, 050402 (2002). https://doi.org/10.1103/PhysRevLett.89.050402,22. P. F. Bedaque, A. Bulgac, G. Rupak, Phys. Rev. A. 68, 033606 (2003). https://doi.org/10.1103/PhysRevA.68.033606 the strength of three-body interactions can dominate over LHY corrections and can be infinite even if the two-body scattering length is finite.11. A. Bulgac, Phys. Rev. Lett. 89, 050402 (2002). https://doi.org/10.1103/PhysRevLett.89.050402 A liquid model based on the Efimov effect11. A. Bulgac, Phys. Rev. Lett. 89, 050402 (2002). https://doi.org/10.1103/PhysRevLett.89.050402,22. P. F. Bedaque, A. Bulgac, G. Rupak, Phys. Rev. A. 68, 033606 (2003). https://doi.org/10.1103/PhysRevA.68.033606 is more robust than the one Petrov envisioned and much more flexible than the van der Waals model. Unlike the quantum liquid droplets created in mixtures of Bose–Einstein condensates,44. C. R. Cabrera et al., Science 359, 301 (2018). https://doi.org/10.1126/science.aao5686 which have practically the same size for particle numbers up to tens of thousands, the quantum liquid droplets I suggested are truly saturating systems, with basically constant interior density. A droplet can have any size, and it can be formed even from a single element. It is a real liquid, with constant density inside and a well-defined surface, and its density and surface tension can be controlled. Also, it is stable against quantum corrections to the mean field.22. P. F. Bedaque, A. Bulgac, G. Rupak, Phys. Rev. A. 68, 033606 (2003). https://doi.org/10.1103/PhysRevA.68.033606Moreover, in a rather special system—an ensemble of spin-polarized tritium atoms—three-body recombination processes are most likely absent.22. P. F. Bedaque, A. Bulgac, G. Rupak, Phys. Rev. A. 68, 033606 (2003). https://doi.org/10.1103/PhysRevA.68.033606,55. D. Blume et al., Phys. Rev. Lett. 89, 163402 (2002). https://doi.org/10.1103/PhysRevLett.89.163402 Although I did not make the estimates, which should be straightforward, I am sure that by controlling the density and thus the rate of four-body recombination, one could create droplets with basically arbitrarily long lifetimes. A droplet of spin-polarized tritium atoms would be a totally unique object, perhaps as unique as macroscopic superfluid helium, but amenable to precise quantum many-body calculations, both static and time-dependent. Quantum turbulence could be studied in a large class of systems, for which a microscopic theory exists, and unlike in the case of superfluid helium, theory could be directly confronted with experiment.Quantum liquid droplets could be either boselets or fermilets and would undergo at least two types of phase transitions, from superfluid to normal and from liquid to gas. Their physics should be fascinating. Mixing bosons and fermions can lead to even more interesting and complex objects.ReferencesSection:ChooseTop of pageReferences <<CITING ARTICLES1. A. Bulgac, Phys. Rev. Lett. 89, 050402 (2002). https://doi.org/10.1103/PhysRevLett.89.050402, Google ScholarCrossref2. P. F. Bedaque, A. Bulgac, G. Rupak, Phys. Rev. A. 68, 033606 (2003). https://doi.org/10.1103/PhysRevA.68.033606, Google ScholarCrossref3. D. S. Petrov, Phys. Rev. Lett. 115, 155302 (2015). https://doi.org/10.1103/PhysRevLett.115.155302, Google ScholarCrossref4. C. R. Cabrera et al., Science 359, 301 (2018). https://doi.org/10.1126/science.aao5686, Google ScholarCrossref5. D. Blume et al., Phys. Rev. Lett. 89, 163402 (2002). https://doi.org/10.1103/PhysRevLett.89.163402, Google ScholarCrossref© 2020 American Institute of Physics.
We investigate the behavior of a two-component Bose-Einstein condensate (BEC) driven by a strong time-dependent resonant magnetic field. The external resonant field couples two hyperfine states via a one-photon transition. It is shown that a first-order parametric instability of a BEC appears if the local atomic number density exceeds a threshold value that is proportional to the driving field. It is shown that the spatial-dependent increment of instability is proportional to the square of the local atomic density. This instability is determined by the nonlinearity of the BEC associated with the short-range interactions between the atoms.