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arXiv:0907.3413 · Physical Review Letters

Parametric Amplification of Vacuum Fluctuations in a Spinor Condensate

Carsten Klempt, O. Topic, Grebremedh Gebreyesus, M. Scherer, T. Henninger, P. Hyllus, Wolfgang A. Ertmer, Luis Santos, J. Arlt

Published May 12, 2010• 85 citations
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Abstract

Parametric amplification of vacuum fluctuations is crucial in modern quantum optics, enabling the creation of squeezing and entanglement. We demonstrate the parametric amplification of vacuum fluctuations for matter waves using a spinor F=2 87Rb condensate. Interatomic interactions lead to correlated pair creation in the mF=±1 states from an initial mF=0 condensate, which acts as a vacuum for mF≠0. Although this pair creation from a pure mF=0 condensate is ideally triggered by vacuum fluctuations, unavoidable spurious initial mF=±1 atoms induce a classical seed which may become the dominant triggering mechanism. We show that pair creation is insensitive to a classical seed for sufficiently large magnetic fields, demonstrating the dominant role of vacuum fluctuations. The presented system thus provides a direct path towards the generation of nonclassical states of matter.

DOI
10.1103/physrevlett.104.195303

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Parametric amplification of vacuum fluctuations is crucial in modern quantum optics, enabling the creation of squeezing and entanglement. We demonstrate the parametric amplification of vacuum fluctuations for matter waves using a spinor F=2 87Rb condensate. Interatomic interactions lead to correlated pair creation in the mF=±1 states from an initial mF=0 condensate, which acts as a vacuum for mF≠0. Although this pair creation from a pure mF=0 condensate is ideally triggered by vacuum fluctuations, unavoidable spurious initial mF=±1 atoms induce a classical seed which may become the dominant triggering mechanism. We show that pair creation is insensitive to a classical seed for sufficiently large magnetic fields, demonstrating the dominant role of vacuum fluctuations. The presented system thus provides a direct path towards the generation of nonclassical states of matter.
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Bose-Einstein condensates of atoms with non-zero spin makes up an ideal system for the study of macroscopic amplification of quantum and classical fluctuations. This study shows that the efficiency of pair creation is influenced by the interplay between the external trapping potential and the Zeeman effect. This reflects the confinement-induced magnetic-field dependence of elementary spin excitations of the trapped condensate. Pair production at these resonances serves as a strong parametric mater-wave amplifier. Results show that pair creation at resonance is triggered by quantum fluctuations. Therefore, in the vacuum state, this system acts as a matter-wave amplifier.
In this paper we discuss Bose-Einstein spinor condensates for F=1F=1F=1 atoms in the context of 87Rb^{87}\text{R}\text{b}87Rb, as studied experimentally by the Stamper-Kurn group [L. E. Sadler et al., Nature (London) 443, 312 (2006)]. The dynamical quantum fluctuations of a sample that starts as a condensate of NNN atoms in a pure F=1F=1F=1, mF=0{m}_{F}=0mF​=0 state are described in analogy to the two-mode squeezing of quantum optics in terms of an su(1,1)\mathfrak{s}\mathfrak{u}(1,1)su(1,1) algebra. In this system the initial mF=0{m}_{F}=0mF​=0 condensate acts as a source (pump) for the creation pairs of ${m}_{F}=1,\ensuremath{-}1$ atoms. We show that even though the system as a whole is described by a pure state with zero entropy, the reduced density matrix for the mF=+1{m}_{F}=+1mF​=+1 degree of freedom, obtained by tracing out the ${m}_{F}=\ensuremath{-}1,0$ degrees of freedom, corresponds to a thermal state. Furthermore, these quantum fluctuations of the initial dynamics of the system provide the seeds for the formation of domains of ferromagnetically aligned spins.
Spin-changing collisions may lead under proper conditions to the parametric amplification of matter waves in spinor Bose-Einstein condensates. Magnetic dipole-dipole interactions, although typically very weak in alkali-metal atoms, are shown to play a very relevant role in the amplification process. We show that these interactions may lead to a strong dependence of the amplification dynamics on the angle between the trap axis and the magnetic-field orientation. We analyze as well the important role played by magnetic-field gradients, which also modify strongly the amplification process. Magnetic-field gradients, hence, must be carefully controlled in future experiments, in order to observe clearly the effects of the dipolar interactions in the amplification dynamics.
Using parametric conversion induced by a Shapiro-type resonance, we produce and characterize a two-mode squeezed vacuum state in a sodium spin 1 Bose-Einstein condensate. Spin changing collisions generate correlated pairs of atoms in the m=±1m=\pm 1m=±1 Zeeman states out of a condensate with initially all atoms in m=0m=0m=0. A novel fluorescence imaging technique with sensitivity ΔN∼1.6\Delta N \sim 1.6ΔN∼1.6 atom enables us to demonstrate the role of quantum fluctuations in the initial dynamics and to characterize the full distribution of the final state, which reaches a squeezing level of 16.8 16.8\,16.8dB.
We have observed parametric generation and amplification of ultracold atom pairs. A 87Rb Bose-Einstein condensate was loaded into a one-dimensional optical lattice with quasimomentum k0 and spontaneously scattered into two final states with quasimomenta k1 and k2 . Furthermore, when a seed of atoms was first created with quasimomentum k1 we observed parametric amplification of scattered atoms pairs in states k1 and k2 when the phase-matching condition was fulfilled. This process is analogous to optical parametric generation (OPG) and amplification (OPA) of photons and could be used to efficiently create entangled pairs of atoms. Furthermore, these results explain the dynamic instability of condensates in moving lattices observed in recent experiments.