We predict that an atomic Bose-Einstein condensate strongly coupled to an intracavity optical lattice can undergo resonant tunneling and directed transport when a constant and uniform bias force is applied. The bias force induces Bloch oscillations, causing amplitude and phase modulation of the lattice which resonantly modifies the site-to-site tunneling. For the right choice of parameters a net atomic current is generated. The transport velocity can be oriented oppositely to the bias force, with its amplitude and direction controlled by the detuning between the pump laser and the cavity. The transport can also be enhanced through imbalanced pumping of the two counterpropagating running wave cavity modes. Our results add to the cold atoms quantum simulation toolbox, with implications for quantum sensing and metrology.
We predict that an atomic Bose-Einstein condensate strongly coupled to an intracavity optical lattice can undergo resonant tunneling and directed transport when a constant and uniform bias force is applied. The bias force induces Bloch oscillations, causing amplitude and phase modulation of the lattice which resonantly modifies the site-to-site tunneling. For the right choice of parameters a net atomic current is generated. The transport velocity can be oriented oppositely to the bias force, with its amplitude and direction controlled by the detuning between the pump laser and the cavity. The transport can also be enhanced through imbalanced pumping of the two counterpropagating running wave cavity modes. Our results add to the cold atoms quantum simulation toolbox, with implications for quantum sensing and metrology.
In this paper we give a new description, in terms of optomechanics, of previous work on the problem of an atomic Bose–Einstein condensate interacting with the optical lattice inside a laser-pumped optical cavity and subject to a bias force, such as gravity. An atomic wave packet in a tilted lattice undergoes Bloch oscillations; in a high-finesse optical cavity the backaction of the atoms on the light leads to a time-dependent modulation of the intracavity lattice depth at the Bloch frequency which can in turn transport the atoms up or down the lattice. In the optomechanical picture, the transport dynamics can be interpreted as a manifestation of dynamical backaction-induced sideband damping/amplification of the Bloch oscillator. Depending on the sign of the pump-cavity detuning, atoms are transported either with or against the bias force accompanied by an up- or down-conversion of the frequency of the pump laser light. We also evaluate the prospects for using the optomechanical Bloch oscillator to make continuous measurements of forces by reading out the Bloch frequency. In this context, we establish the significant result that the optical spring effect is absent and the Bloch frequency is not modified by the backaction.
Particles in a perfect lattice potential perform Bloch oscillations when subject to a constant force, leading to localization and preventing conductivity. For a weakly interacting Bose-Einstein condensate of Cs atoms, we observe giant center-of-mass oscillations in position space with a displacement across hundreds of lattice sites when we add a periodic modulation to the force near the Bloch frequency. We study the dependence of these "super" Bloch oscillations on lattice depth, modulation amplitude, and modulation frequency and show that they provide a means to induce linear transport in a dissipation-free lattice.
This article complements previous work on the nondestructive observation of Bloch oscillations of a Bose-Einstein condensate in an optical lattice formed inside a high-finesse optical cavity [H. Ke\ss{}ler et al., New J. Phys. 18, 102001 (2016)]. We present measurements showing that the observed Bloch frequency is independent of the atom number and hence the cooperative coupling strength, the intracavity lattice depth, and the detuning between the external pump light and the effective cavity resonance. We find that in agreement with theoretical predictions, despite the atom-cavity dynamics, the value of the Bloch frequency agrees with that expected in conventional optical lattices, where it solely depends on the sizes of the force and the lattice constant. We also show that Bloch oscillations are observed in a self-organized two-dimensional lattice, which is formed if, instead of axially pumping the cavity through one of its mirrors, the Bose-Einstein condensate is irradiated by an optical standing wave oriented perpendicularly with respect to the cavity axis. For this case, however, excessive decoherence prevents a meaningful quantitative assessment.
We show theoretically that the dynamics of cold atoms in the lowest-energy band of a stationary optical lattice can be transformed and controlled by a second, weaker, periodic potential moving at a constant speed along the axis of the stationary lattice. The atom trajectories exhibit complex behavior, which depends sensitively on the amplitude and speed of the propagating lattice. When the speed and amplitude of the moving potential are low, the atoms are dragged through the static lattice and perform drifting orbits with frequencies an order of magnitude higher than that corresponding to the moving potential. Increasing either the speed or amplitude of the moving lattice induces Bloch-like oscillations within the energy band of the static lattice, which exhibit complex resonances at critical values of the system parameters. In some cases, a very small change in these parameters can reverse the atom's direction of motion. In order to understand these dynamics we present an analytical model, which describes the key features of the atom transport and also accurately predicts the positions of the resonant features in the atom's phase space. The abrupt controllable transitions between dynamical regimes, as well as the associated set of resonances, provide a mechanism for transporting atoms between precise locations in a lattice, as required for using cold atoms to simulate condensed matter or as a stepping stone to quantum information processing. The system also provides a direct quantum simulator of acoustic waves propagating through semiconductor nanostructures in sound analogs of the optical laser (saser).
Ultracold atoms in an optical lattice Bloch oscillate when subject to a constant force. In the first work presented in this thesis we have theoretically studied the scenario where the optical lattice potential is provided by the electric field inside an optical cavity. The coherent atom-light interaction in a cavity gives rise to a backaction effect on the light field which can modify the intracavity field amplitude and phase. In our first treatment of this problem we model the cavity light field and atoms by classical fields and solve the coupled atom-light equations of motion. As a result, we find that the amplitude and phase of the transmitted light field is modulated at the Bloch frequency. Remarkably, the Bloch frequency itself is not modified by the backaction. Thus the transmitted light field can be used to observe the oscillations continuously, allowing high-precision measurement with small clouds of atoms. In the second problem presented in this thesis, we explore the band structure of the steady state solutions of the atom-cavity system. A crucial first step towards determining the band structure is the identification of an energy functional that describes the coupled atom-light system. Although, we do not include direct atom-atom interactions in our models, the coupling of the atoms to the single mode light field of the cavity introduces an effective mutual interaction which is correctly taken into account by the energy functional we introduce. Corresponding to each point in the band there exists a steady state light field associated with an average cavity photon number. The dispersive nonlinear atom-light interaction can lead to bistable solutions for this intracavity photon number. For parameters where the atom-cavity system exhibits bistability, the atomic band structure develops loop structures akin to the ones predicted for Bose-Einstein condensates in ordinary (non-cavity) optical lattices. However, in our case the nonlinearity derives from the cavity backaction rather than from direct interatomic interactions. We find both bi- and tri-stable regimes associated with the lowest band, and show that the multistability we observe can be analysed in terms of swallowtail catastrophes. Dynamic and energetic stability of the meanfield solutions is also studied, and we show that the bistable solutions have, as expected, one unstable and two stable branches. The presence of loops in the band structure can lead to a breakdown in adiabaticity during Bloch oscillations as the entire band is sampled during the dynamics. We therefore use the insight gleaned from this work in choosing parameters for the Bloch oscillation measurement proposal presented in the rest of the thesis. In the third work presented in the thesis, we go beyond the mean field description and consider effects of the quantised nature of the light and atomic fields. The cavity light field is always in contact with external electromagnetic fields through the partially transmissive mirrors. This coupling to the external modes enters as quantum noise in the dynamics of the intracavity field and can also be viewed as a manifestation of quantum measurement backaction corresponding to the continuous observation of the transmitted light field. We solve the Heisenberg-Langevin equations for linearized fluctuations about the atomic and optical meanfields and examine how this influences the signal-to-noise ratio of a measurement of external forces using this system. In particular, we investigate the effects of changing the number of atoms, the intracavity lattice depth, and the atom-light coupling strength, and show how resonances between the Bloch oscillation dynamics and the quasiparticle spectrum have a strong influence on the signal-to-noise ratio as well as heating effects. One of the hurdles we overcome along the way is the proper treatment of fluctuations about time-dependent meanfields in the context of cold atom cavity-QED.
Cold atoms in an optical lattice execute Bloch-Zener oscillations when they are accelerated. We have performed a theoretical investigation into the case when the optical lattice is the intracavity field of a driven Fabry-Perot resonator. When the atoms oscillate inside the resonator, we find that their back-action modulates the phase and intensity of the light transmitted through the cavity. We solve the coupled atom-light equations self-consistently and show that, remarkably, the Bloch period is unaffected by this back-action. The transmitted light provides a way to observe the oscillation continuously, allowing high-precision measurements to be made with a small cloud of atoms.