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arXiv:1404.2546 · Laser Physics Letters

Mode-locked Bloch oscillations in a ring cavity

Marina Samoylova, N. Piovella, Dominic Hunter, Gordon R. M. Robb, Romain Bachelard, Ph. W. Courteille

Published Nov 12, 2014• 10 citations
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Abstract

We present a new technique for stabilizing and monitoring Bloch oscillations of ultracold atoms in an optical lattice under the action of a constant external force. In the proposed scheme, the atoms also interact with a unidirectionally pumped optical ring cavity whose one arm is collinear with the optical lattice. For weak collective coupling, Bloch oscillations dominate over the collective atomic recoil lasing instability and develop a synchronized regime in which the atoms periodically exchange momentum with the cavity field.

DOI
10.1088/1612-2011/11/12/126005

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We consider Bloch oscillations of ultracold atoms stored in a one-dimensional vertical optical lattice and simultaneously interacting with a unidirectionally pumped optical ring cavity whose vertical arm is collinear with the optical lattice. We find that the feedback provided by the cavity field on the atomic motion synchronizes Bloch oscillations via a mode-locking mechanism, steering the atoms to the lowest Bloch band. It also stabilizes Bloch oscillations against noise, and even suppresses dephasing due to atom-atom interactions. Furthermore, it generates periodic bursts of light emitted into the counter-propagating cavity mode, providing a non-destructive monitor of the atomic dynamics. All these features may be crucial for future improvements of the design of atomic gravimeters based on recording Bloch oscillations.

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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.

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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.

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We present a new technique for stabilizing and monitoring Bloch oscillations of ultracold atoms in an optical lattice under the action of a constant external force. In the proposed scheme, the atoms also interact with a unidirectionally pumped optical ring cavity whose one arm is collinear with the optical lattice. For weak collective coupling, Bloch oscillations dominate over the collective atomic recoil lasing instability and develop a synchronized regime in which the atoms periodically exchange momentum with the cavity field.
We consider Bloch oscillations of ultracold atoms stored in a one-dimensional vertical optical lattice and simultaneously interacting with a unidirectionally pumped optical ring cavity whose vertical arm is collinear with the optical lattice. We find that the feedback provided by the cavity field on the atomic motion synchronizes Bloch oscillations via a mode-locking mechanism, steering the atoms to the lowest Bloch band. It also stabilizes Bloch oscillations against noise, and even suppresses dephasing due to atom-atom interactions. Furthermore, it generates periodic bursts of light emitted into the counter-propagating cavity mode, providing a non-destructive monitor of the atomic dynamics. All these features may be crucial for future improvements of the design of atomic gravimeters based on recording Bloch oscillations.
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.
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.
The work developed in this thesis investigate the dynamics of ultracold atoms trapped in a ring cavity and undergoing Bloch oscillations due to the influence of a one-dimensional vertical optical lattice and of the gravitational force.In this configuration, the atoms collectively scatter light from the pump into the copropagating cavity mode, which then leads to a self-consistent grating of the matter: this mechanism was coined collective atomic recoil lasing (CARL).Such interaction between atomic motion and cavity modes provides a possible continuous and non-destructive method to monitor the Bloch oscillations dynamics, which could be implemented in atomic gravimeters.This dissertation investigates the fundamental problem of dissipation effects due to spontaneous emission of the atoms, which is responsible for a suppression of the Bloch oscillations signatures on the light modes.We also study a possible solution for this issue by including a third atomic level in the configuration to explore a probable dissipation reduction due to the phenomenon of electromagnetically induced transparency (EIT).
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 describe a scheme for probing a gas of ultracold atoms trapped in an optical lattice and moving in the presence of an external potential. The probe is nondestructive and uses the existing lattice fields as the measurement device. Two counterpropagating cavity fields simultaneously set up a conservative lattice potential and a weak quantum probe of the atomic motion. Balanced heterodyne detection of the probe field at the cavity output along with integration in time and across the atomic cloud yield information about the atomic dynamics in a single run. The scheme is applied to a measurement of the Bloch oscillation frequency for atoms moving in the presence of the local gravitational potential. Signal-to-noise ratios are estimated to be as high as 104{10}^{4}104.