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Laser Physics

Resonant amplification of quantum fluctuations in a spinor gas

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

Published Apr 2, 2010• 4 citations
Publisher

Abstract

Bose-Einstein condensates of atoms with non-zero spin are known to constitute an ideal system to investigate fundamental properties of magnetic superfluids. More recently it was realized that they also provide the fascinating opportunity to investigate the macroscopic amplification of quantum and classical fluctuations. This is strikingly manifested in a sample initially prepared in the m F = 0 state, where spin-changing collisions triggered by quantum fluctuations may lead to the creation of correlated pairs in m F = ±1. We show that the pair creation efficiency is strongly influenced by the interplay between the external trapping potential and the Zeeman effect. It thus reflects the confinement-induced magnetic field dependence of elementary spin excitations of the condensate. Remarkably, pair production in our experiments is therefore characterized by a multi-resonant dependence on the magnetic field. Pair creation at these resonances acts as strong parametric matter-wave amplifier. Depending on the resonance condition, this amplification can be extremely sensitive or insensitive to the presence of seed atoms. We show that pair creation at a resonance which is insensitive to the presence of seed atoms is triggered purely by quantum fluctuations and thus the system acts as a matter-wave amplifier for the vacuum state.

DOI
10.1134/s1054660x10090422

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Bose-Einstein condensates of atoms with non-zero spin are known to constitute an ideal system to investigate fundamental properties of magnetic superfluids. More recently it was realized that they also provide the fascinating opportunity to investigate the macroscopic amplification of quantum and classical fluctuations. This is strikingly manifested in a sample initially prepared in the m F = 0 state, where spin-changing collisions triggered by quantum fluctuations may lead to the creation of correlated pairs in m F = ±1. We show that the pair creation efficiency is strongly influenced by the interplay between the external trapping potential and the Zeeman effect. It thus reflects the confinement-induced magnetic field dependence of elementary spin excitations of the condensate. Remarkably, pair production in our experiments is therefore characterized by a multi-resonant dependence on the magnetic field. Pair creation at these resonances acts as strong parametric matter-wave amplifier. Depending on the resonance condition, this amplification can be extremely sensitive or insensitive to the presence of seed atoms. We show that pair creation at a resonance which is insensitive to the presence of seed atoms is triggered purely by quantum fluctuations and thus the system acts as a matter-wave amplifier for the vacuum state.
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.
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.
We analyze the spinor dynamics of a 87Rb F=2 condensate initially prepared in the m(F) = 0 Zeeman sublevel. We show that this dynamics, characterized by the creation of correlated atomic pairs in m(F) = +/-1, presents an intriguing multiresonant magnetic-field dependence induced by the trap inhomogeneity. This dependence is directly linked to the most unstable Bogoliubov spin excitations of the initial m(F) = 0 condensate, showing that, in general, even a qualitative understanding of the pair-creation efficiency in a spinor condensate requires a careful consideration of the confinement.
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.
Abstract The ability to cool quantum gases into the quantum degenerate realm has opened up possibilities for an extreme level of quantum-state control. In this paper, we investigate one such control protocol that demonstrates the resonant amplification of quasimomentum pairs from a Bose–Einstein condensate by the periodic modulation of the two-body s-wave scattering length. This shows a capability to selectively amplify quantum fluctuations with a predetermined momentum, where the momentum value can be spectroscopically tuned. A classical external field that excites pairs of particles with the same energy but opposite momenta is reminiscent of the coherently-driven nonlinearity in a parametric amplifier crystal in nonlinear optics. For this reason, it may be anticipated that the evolution will generate a ‘squeezed’ matter-wave state in the quasiparticle mode on resonance with the modulation frequency. Our model and analysis is motivated by a recent experiment by Clark et al that observed a time-of-flight pattern similar to an exploding firework (Clark et al 2017 Nature 551 356–9). Since the drive is a highly coherent process, we interpret the observed firework patterns as arising from a monotonic growth in the two-body correlation amplitude, so that the jets should contain correlated atom pairs with nearly equal and opposite momenta. We propose a potential future experiment based on applying Ramsey interferometry to experimentally probe these pair correlations.
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=±1 Zeeman states out of a condensate with initially all atoms in m=0. A novel fluorescence imaging technique with sensitivity ΔN∼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. Assuming that all atoms share the same spatial wave function, we infer a squeezing parameter of 15.3 dB.