Abstract
It is shown that there exist both dynamically stable and unstable dilute-gas Bose–Einstein condensates that, in the hydrodynamic limit, exhibit a behavior completely analogous to that of gravitational black holes. The dynamical instabilities involve creation of quasiparticle pairs in positive and negative energy states. We illustrate these features in two qualitatively different one-dimensional models. We have also simulated the creation of a stable sonic black hole by solving the Gross–Pitaevskii equation numerically for a condensate subject to a trapping potential that is adiabatically deformed. A sonic black hole could in this way be created experimentally with state-of-the-art or planned technology.
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REFERENCES
Anderson, M. H., Ensher, J. R., Matthews, M. R., Wieman, C. E., and Cornell, E. A. (1995). Observation of Bose-Einstein condensation in a dilute atomic vapor, Science 269, 198.
Andrews, M. R., Townsend, C. G., Miesner, H.-J., Durfee, D. S., Kurn, D. M., and Ketterle W. (1997). Observation of interference between two Bose condensates, Science 275, 637.
Bloch, I., Hänsch, T.W., and Esslinger, T. (1999). An Atom Laser with a cw Output Coupler, Physical Review Letters 82, 3008.
Burger, S., Bongs, K., Dettmer, S., Ertmer, W., Sengstock, K., Sanpera, A., Shlyapnikov, G. V., and Lewenstein, M. (1999). Dark Solitons in Bose-Einstein Condensates, Physical Review Letters 83, 5198.
Corley, S. (1998). Computing the spectrum of black hole radiation in the presence of high frequency dispersion: An analytical approach, Physical Review D 57, 6280.
Corley, S. and Jacobson, T. (1999). Black hole lasers, Physical Review D 59, 4011.
Dalfovo, F., Giorgini, S., Pitaevskii, L. P., and Stringari, S. (1999). Theory of Bose-Einstein condensation in trapped gases, Reviews of Modern Physics 71, 463.
Davis, K. B., Mewes, M.-O., Andrews, M. R., van Druten N. J., Durfee, D. S., Kurn, D. M., and Ketterle, W. (1995). Bose-Einstein Condensation in a Gas of Sodium Atoms, Physical Review Letters 75, 3969.
Deng, L., Hagley, E.W., Wen, J., Trippenbach, M., Band, Y., Julienne, P. S., Simsarian J. E., Helmerson, K., Rolston, S. L., Phillips, W. D. (1999). Four-wave mixing with matter waves, Nature (London) 398, 218.
Dum, R., Cirac, J. I., Lewenstein, M., and Zoller, P. (1998). Creation of Dark Solitons and Vortices in Bose-Einstein Condensates, Physical Review Letters 80, 2972.
Fedichev, P. O. and Shlyapnikov, G. V. (1999). Dissipative dynamics of a vortex state in a trapped Bose-condensed gas, Physical Review A 60, R1779.
Fulling, S. A. (1989). Aspects of Quantum Field Theory in Curved Spacetime, Cambridge University Press, Cambridge.
Garay, L. J., Anglin, J. R., Cirac, J. I., and Zoller, P. (2000). Sonic Analog of Gravitational Black Holes in Bose-Einstein Condensates, Physical Review Letters 85, 4643
Garay, L. J., Anglin, J. R., Cirac, J. I., and Zoller, P. (2001). Sonic black holes in dilute Bose-Einstein condensates, Physical Review A 63, 023611.
Garay, L. J., Anglin, J. R., Cirac, J. I., and Zoller, P. (unpublished). Unpublished manuscript.
Hagley, E. W., Deng, L., Kozuma, M., Wen, J., Helmerson, K., Rolston, S. L., and Philips, W. D. (1999). A Well-Collimated Quasi-Continuous Atom Laser, Science 283, 1706.
Hawking, S. W. (1974). Black holes explosions? Nature (London) 248, 30.
Hawking, S.W. (1975). Particle creation by black hole, Communications in Mathematical Physics 43, 199.
Jacobson, T. (1991). Black-hole evaporation and ultrashort distances, Physical Review D 44, 1731.
Jacobson, T. (1999). Trans-Planckian redshifts and the substance of the space-time river, Progress of Theoretical Physics 136(Suppl.), 1.
Jacobson, T. A. and Volovik, G. E. (1998). Event horizons and ergoregions in 3He, Physical Review D 58, 4021.
Kang, G. (1996). Preprint hep-th/9603166. unpublished manuscript. See for a concise pedagogical illustration, and references therein.
Leonhardt, U. and Piwnicki, P. (1999). Optics of nonuniformly moving media, Physical Review A 60, 4301.
Leonhardt, U. and Piwnicki, P. (2000). Relativistic Effects of Light in Moving Media with Extremely Low Group Velocity, Physical Review Letters 84, 822.
Liberati, S., Sonego, S., and Visser, M. (2000). Unexpectedly large surface gravities for acoustic horizons? Classical Quantum Gravity 17, 2903.
Matthews, M. R., Anderson, B. P., Haljan, P. C., Hall, D. S., Wieman, C. E., and Cornell, E. A. (1999). Vortices in a Bose-Einstein Condensate, Physical Review Letters 83, 2498.
Misner, C. W., Thorne, K. S., and Wheeler, J. A. (1973). Gravitation, Freeman, San Francisco.
Reznik, B. (1997). Preprint gr-qc/9703076. Unpublished manuscript.
Ruutu, V. M., Eltsov, V. B., Gill, A., Kibble, T.W., Krusius, M., Makhlin, Yu. G., Placais, B., Volovik, G. E., Wen, Xu. (1996). Vortex formation in neutron-irradiated superfluid 3He as an analogue of cosmological defect formation, Nature (London) 382, 334.
Schroer, B. and Swieca, J. A. (1970). Indefinite Metric and Stationary external Interactions of Quantized Fields, Physical Review D 2, 2938.
Unruh, W. G. (1981). Experimental Black-Hole Evaporation? Physical Review Letters 46, 1351.
Unruh, W. G. (1995). Sonic analogue of black holes and the effects of high frequencies on black hole evaporation, Physical Review D 51, 2827.
Visser, M. (1998a). Hawking Radiation without Black Hole Entropy, Physical Review Letters 80, 3436.
Visser, M. (1998b). Acoustic black holes: horizons, ergospheres, and Hawking radiation, Classical Quantum Gravity 15, 1767.
Visser, M. (1993). Preprint gr-qc/9311028. Unpublished manuscript.
Volovik, G. E. (1999a). Simulation of Painleve-Gullstrand black hole in thin 3He A film, Pis'mav Zhurnal Eksperimental'noi i Teoreticheskoi Fiziki 69, 662.
Volovik, G. E. (1999b). Simulation of Painleve-Gullstrand black hole in thin 3He A film, JETP Letters 69, 705.
Williams, J. and Holland, M. (1999). Preparing topological states of a Bose-Einstein condensate, Nature (London) 401, 568.
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Garay, L.J. Black Holes in Bose–Einstein Condensates. International Journal of Theoretical Physics 41, 2073–2090 (2002). https://doi.org/10.1023/A:1021172708149
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DOI: https://doi.org/10.1023/A:1021172708149