Ian D. Leroux

Implementation of Cavity Squeezing of a Collective Atomic Spin

We squeeze unconditionally the collective spin of a dilute ensemble of laser-cooled 87Rb atoms using their interaction with a driven optical resonator. The shape and size of the resulting spin uncertainty region are well described by a simple analytical model [M. H. Schleier-Smith, I. D. Leroux, and V. Vuletić, arXiv:0911.3936 [Phys. Rev. A (to be published)]] through 2 orders of magnitude in the effective interaction strength, without free parameters. We deterministically generate states with up to 5.6(6) dB of metrologically relevant spin squeezing on the canonical 87Rb hyperfine clock transition.

States of an Ensemble of Two-Level Atoms with Reduced Quantum Uncertainty

We generate entangled states of an ensemble of 5x10{4} 87Rb atoms by optical quantum nondemolition measurement. The resonator-enhanced measurement leaves the atomic ensemble, prepared in a superposition of hyperfine clock levels, in a squeezed spin state. By comparing the resulting reduction of quantum projection noise [up to 8.8(8) dB] with the concomitant reduction of coherence, we demonstrate a clock input state with spectroscopic sensitivity 3.0(8) dB beyond the standard quantum limit.

Interaction between Atomic Ensembles and Optical Resonators: Classical Description

Abstract Many effects in the interaction between atoms and a cavity that are usually described in quantum mechanical terms (cavity quantum electrodynamics, cavity QED) can be understood and quantitatively analyzed within a classical framework. We adopt such a classical picture of a radiating dipole oscillator to derive explicit expressions for the coupling of single atoms and atomic ensembles to Gaussian modes in free space and in an optical resonator. The cooperativity parameter of cavity QED is shown to play a central role and is given a geometrical interpretation. The classical analysis yields transparent, intuitive results that are useful for analyzing applications of cavity QED such as atom detection and counting, cavity cooling, cavity spin squeezing, cavity spin optomechanics, or phase transitions associated with the self-organization of the ensemble-light system.

Optomechanical cavity cooling of an atomic ensemble.

We demonstrate cavity sideband cooling of a single collective motional mode of an atomic ensemble down to a mean phonon occupation number ⟨n⟩(min⁡)=2.0(-0.3)(+0.9). Both ⟨n⟩(min) and the observed cooling rate are in good agreement with an optomechanical model. The cooling rate constant is proportional to the total photon scattering rate by the ensemble, demonstrating the cooperative character of the light-emission-induced cooling process. We deduce fundamental limits to cavity cooling either the collective mode or, sympathetically, the single-atom degrees of freedom.

Collective State Measurement of Mesoscopic Ensembles with Single-Atom Resolution

We demonstrate single-atom resolution, as well as detection sensitivity more than 20 dB below the quantum projection noise limit, for hyperfine-state-selective measurements on mesoscopic ensembles containing 100 or more atoms. The measurement detects the atom-induced shift of the resonance frequency of an optical cavity containing the ensemble. While spatially varying coupling of atoms to the cavity prevents the direct observation of a quantized signal, the demonstrated measurement resolution provides the readout capability necessary for atomic interferometry substantially below the standard quantum limit and down to the Heisenberg limit.

Chapter 4 – Interaction between Atomic Ensembles and Optical Resonators: Classical Description

Abstract Many effects in the interaction between atoms and a cavity that are usually described in quantum mechanical terms (cavity quantum electrodynamics, cavity QED) can be understood and quantitatively analyzed within a classical framework. We adopt such a classical picture of a radiating dipole oscillator to derive explicit expressions for the coupling of single atoms and atomic ensembles to Gaussian modes in free space and in an optical resonator. The cooperativity parameter of cavity QED is shown to play a central role and is given a geometrical interpretation. The classical analysis yields transparent, intuitive results that are useful for analyzing applications of cavity QED such as atom detection and counting, cavity cooling, cavity spin squeezing, cavity spin optomechanics, or phase transitions associated with the self-organization of the ensemble-light system.

Pinning an Ion with an Intracavity Optical Lattice

We report one-dimensional pinning of a single ion by an optical lattice. A standing-wave cavity produces the lattice potential along the rf-field-free axis of a linear Paul trap. The ions localization is detected by measuring its fluorescence when excited by standing-wave fields with the same period, but different spatial phases. The experiments agree with an analytical model of the localization process, which we test against numerical simulations. For the best localization achieved, the ions average coupling to the cavity field is enhanced from 50% to 81(3)% of its maximum possible value, and we infer that the ion is bound in a lattice well with over 97% probability.

Analysis of thermal radiation in ion traps for optical frequency standards

In many of the high-precision optical frequency standards with trapped atoms or ions that are under development to date, the AC Stark shift induced by thermal radiation leads to a major contribution to the systematic uncertainty. We present an analysis of the inhomogeneous thermal environment experienced by ions in various types of ion traps. Finite element models which allow the determination of the temperature of the trap structure and the temperature of the radiation were developed for 5 ion trap designs, including operational traps at PTB and NPL and further optimized designs. Models were refined based on comparison with infrared camera measurement until an agreement of better than 10% of the measured temperature rise at critical test points was reached. The effective temperature rises of the radiation seen by the ion range from 0.8 K to 2.1 K at standard working conditions. The corresponding fractional frequency shift uncertainties resulting from the uncertainty in temperature are in the 10-18 range for optical clocks based on the Sr+ and Yb+ E2 transitions, and even lower for Yb+ E3, In+ and Al+. Issues critical for heating of the trap structure and its predictability were identified and design recommendations developed.

Precision spectroscopy by photon-recoil signal amplification

Precision spectroscopy of atomic and molecular ions offers a window to new physics, but is typically limited to species with a cycling transition for laser cooling and detection. Quantum logic spectroscopy has overcome this limitation for species with long-lived excited states. Here we extend quantum logic spectroscopy to fast, dipole-allowed transitions and apply it to perform an absolute frequency measurement. We detect the absorption of photons by the spectroscopically investigated ion through the photon recoil imparted on a co-trapped ion of a different species, on which we can perform efficient quantum logic detection techniques. This amplifies the recoil signal from a few absorbed photons to thousands of fluorescence photons. We resolve the line centre of a dipole-allowed transition in (40)Ca(+) to 1/300 of its observed linewidth, rendering this measurement one of the most accurate of a broad transition. The simplicity and versatility of this approach enables spectroscopy of many previously inaccessible species.

Quantum Algorithmic Readout in Multi-Ion Clocks

Optical clocks based on ensembles of trapped ions promise record frequency accuracy with good short-term stability. Most suitable ion species lack closed transitions, so the clock signal must be read out indirectly by transferring the quantum state of the clock ions to cotrapped logic ions of a different species. Existing methods of quantum logic readout require a linear overhead in either time or the number of logic ions. Here we describe a quantum algorithmic readout whose overhead scales logarithmically with the number of clock ions in both of these respects. The scheme allows a quantum nondemolition readout of the number of excited clock ions using a single multispecies gate operation which can also be used in other areas of ion trap technology such as quantum information processing, quantum simulations, metrology, and precision spectroscopy.