A quantum particle moving in a periodic potential, with periodicity d, when acted by an external constant force F undergoes the dynamical phenomenon of Bloch-Zener oscillations (BZO). We investigate BZO of a neutral cold atom in an optical cavity pumped by a laser. We find that the single mode electromagnetic field of the optical cavity is affected by the atomic dynamics and propose the idea that a measurement of the electromagnetic field leaking out of the cavity will reflect the BZO frequency WB = Fd/h, and can be used for a precision measurement of F. The motivation for such a study comes from the fact that if the force F is gravity, then one can probe gravitational forces on sub-millimeter scales since the size of these systems are generally a few hundreds of microns. Such a study can be used to detect deviations from Newtonian gravity at short range proposed by some theories beyond the standard model of particle physics.
A quantum particle moving in a periodic potential, with periodicity d, when acted by an external constant force F undergoes the dynamical phenomenon of Bloch-Zener oscillations (BZO). We investigate BZO of a neutral cold atom in an optical cavity pumped by a laser. We find that the single mode electromagnetic field of the optical cavity is affected by the atomic dynamics and propose the idea that a measurement of the electromagnetic field leaking out of the cavity will reflect the BZO frequency WB = Fd/h, and can be used for a precision measurement of F. The motivation for such a study comes from the fact that if the force F is gravity, then one can probe gravitational forces on sub-millimeter scales since the size of these systems are generally a few hundreds of microns. Such a study can be used to detect deviations from Newtonian gravity at short range proposed by some theories beyond the standard model of particle physics.
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.
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.
We extend our theory of Bloch oscillations of cold atoms inside an optical cavity [Venkatesh et al., Phys. Rev. A 80, 063834 (2009)] to include the effects of quantum noise arising from coupling to external modes. The noise acts as a form of quantum measurement backaction by perturbing the coupled dynamics of the atoms and the light. We take it into account by solving the Heisenberg-Langevin equations for linearized fluctuations about the atomic and optical mean fields 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 in this paper is the proper treatment of fluctuations about time-dependent mean fields 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 intra-cavity 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.
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.
The work presented in this thesis is dedicated to studies of stabilization of Bloch oscillations of ultracold atoms in a one-dimensional vertical optical lattice under the influence of the gravitational force. The atoms simultaneously interact with both the lattice potential and a unidirectionally pumped optical ring cavity whose vertical arm is collinear with the optical lattice. In the proposed scheme, the atoms not only exchange photons between the optical lattice laser beams, but also collectively scatter light from the pump into the reverse cavity mode. The initial investigation of the system without the cavity allows understanding of the importance of the perfectly adiabatic atomic motion in the observation of stable Bloch oscillations and how easily the adiabaticity can be broken due to a very fast switch-on of the lattice or its amplitude and phase modulation. Under certain parameter regimes, adding the ring cavity to the system provides a surprisingly positive feedback on the atomic dynamics. It is found that, while acting back on the atoms, the cavity field establishes a mode-locking mechanism which assists adiabatic rapid passages between adjacent momentum states. Thus, the cavity-induced feedback mechanism enforces the adiabaticity of the process and reveals a regime where the Bloch oscillations are self-synchronized for long times. This stabilization technique is shown to steer the atoms to the lowest Bloch band preventing the problem of interband tunneling. A demonstration is also made of the ability of the system to stabilize the atomic Bloch oscillations against technical amplitude or phase noise and even suppress dephasing due to the atom-atom interactions. Furthermore, the response of the system to the atomic motion is generated in the form of perfectly detectable periodic bursts of light emitted into the counter-propagating cavity mode. Thus, the system offers a continuous and reliable non-destructive method to monitor the Bloch oscillations dynamics without perturbing their periodicity by detecting the scattered light transmitted through the cavity. All features studied in this work may be crucial for future improvements of the design of atomic gravimeters based on recording Bloch oscillations.