Rectified Momentum Transport for a Kicked Bose-Einstein Condensate

Abstract

We report the experimental observation of rectified momentum transport for a Bose-Einstein Condensate kicked at the Talbot time (quantum resonance) by an optical standing wave. Atoms are initially prepared in a superposition of the 0 and −2 k l momentum states using an optical π/2 pulse. By changing the relative phase of the superposed states, a momentum current in either direction along the standing wave may be produced. We offer an interpretation based on matter wave interference, showing that the observed effect is uniquely quantum.The current interest in rectified atomic diffusion, or atomic ratchets, may be traced back to fundamental thermodynamical concerns [1] and also the desire to understand the so-called "Brownian motors" linked to directed diffusion on a molecular scale [2,3]. Abstractly, the ratchet effect may be defined as the inducement of directed diffusion in a system subject to unbiased perturbations due to a broken spatio-temporal symmetry.Given the scale on which such microscopic ratchets must work, it is not surprising that the concept of quantum ratchets has recently augmented this area of investigation. The addition of quantum effects such as tunneling gives rise to new ratchet phenomena such as current reversal [4]. Whilst early quantum ratchet investigations, both theoretical and experimental, have focussed on the role of dissipative fluctuations in driving a ratchet current [5], recent theory has considered the possibility of Hamiltonian ratchets, where the diffusion arises from Hamiltonian chaos rather than stochastic fluctuations [6]. This has lead to proposals [7,8] and even an experimental realisation [9] for ratchet systems realised using atom optics, in the context of the atom optics kicked rotor [10] where periodic pulses from an optical standing wave kick atoms into different momentum states.It is generally accepted that a ratchet effect cannot be produced without breaking the spatio-temporal symmetry of the kicked rotor system. In Ref.[9], a rocking sine wave potential was combined with broken time symmetry of the kicking pulses to effectively realise such a system in an experiment. Other schemes involve the use of quantum resonance (QR) to drive the ratchet effect. At QR, atoms typically exhibit linear momentum growth symmetrical about the initial mean momentum. However it has been suggested that merely breaking the spatial symmetry of the kicked rotor at QR may be sufficient to produce a ratchet current [11]. In this letter we present the first experimental evidence of such a resonant ratchet effect in which the underlying mechanism is purely quantum. Our system uses a Bose-Einstein condensate (BEC) kicked by an optical standing wave [12], but there is no asymmetry in either the kicking potential * Electronic address: mark@ils.uec.ac.jp or the period of the kicks, (which is set to the Talbot time T T corresponding to quantum resonance [13]). Rather, the observed directed diffusion is a property of the initial atomic wavefunction (which we prepare before kicking) in the presenc...

Artificial Brownian motors: Controlling transport on the nanoscale

“…For a ␦-kicked rotor model with time symmetry broken by a two-period kicking cycle ͑asymmetric temporal drive͒, directed growth of momentum has been detected by Jones et al ͑2007͒. For a phase-dependent initial preparation of a Bose-Einstein condensate kicked at resonance, a momentum acceleration has been observed by Sadgrove et al ͑2007͒ at zero quasimomentum, while for an arbitrary quasimomentum directed quantum Brownian transport has been realized by Dana et al ͑2008͒. The last experiment also showed that the intrinsic experimentally nonavoidable finite width in quasimomentum causes a suppression of the acceleration, eventually leading to a saturation effect after short times.…”

Cooling by Time Reversal of Atomic Matter Waves

“…The reversed peak is very sensitive to variations of and other parameters breaking time reversal symmetry, and therefore this setup can be used as a sensitive Loschmidt interferometer to explore such a symmetry breaking (e.g., a gravitational field component along the optical lattice gives a shift in which affects the Loschmidt peak). The parameters considered here are well accessible to nowadays experimental setups (see, e.g., [13][14][15][16][17][18][19][20] ). The realization of our proposal will shed a new light on the long-standing Boltzmann-Loschmidt dispute on time reversibility.…”

“…This model has been built up experimentally with cold atoms in kicked optical lattices [13][14][15][16]. Recent progress allowed to implement this model with ultracold atoms and Bose-Einstein condensates (BEC) [17][18][19][20], with high-precision subrecoil definition of the momentum of the atoms, allowing, for example, to observe [17,19] high order quantum resonances [21]. We show that these experimental techniques allow to perform time reversal for a significant part of the atoms.…”

Environmental stability of quantum chaotic ratchets

“…Cold atoms in optical lattices are one of the main examples of successful implementations and theoretical developments [11,12]. Also, Bose-Einstein condensates have been transported (for particular initial conditions) by using purely quantum ratchet accelerators [13]. In this case, the current has no classical counterpart [14], and the energy grows ballistically [15,16].…”