arXiv subjects

A. D. Boozer

Publications and source records attributed to A. D. Boozer.

14 recordsLinked to original sources

arXiv2011

Time-optimal synthesis of SU(2) transformations for a spin-1/2 system

We consider a quantum control problem involving a spin-1/2 particle in a magnetic field. The magnitude of the field is held constant, and the direction of the field, which is constrained to lie in the x-y plane, serves as a control parameter that can be varied to govern the evolution of the system. We analytically solve for the time dependence of the control parameter that will synthesize a given target SU(2) transformation in the least possible amount of time, and we show that the time-optimal solutions have a simple geometric interpretation in terms of the fiber bundle structure of SU(2). We also generalize our time-optimal solutions to a control problem that includes a constant bias field along the z axis, and to the case of inhomogeneous control, in which a single control parameter governs the evolution of an ensemble of spin-1/2 systems.

quant-ph↗

arXiv2008

Advanced action in classical electrodynamics

The time evolution of a charged point particle is governed by a second-order integro-differential equation that exhibits advanced effects, in which the particle responds to an external force before the force is applied. In this paper we give a simple physical argument that clarifies the origin and physical meaning of these advanced effects, and we compare ordinary electrodynamics with a toy model of electrodynamics in which advanced effects do not occur.

physics.class-ph↗

arXiv2008

Theory of Raman transitions in cavity QED

We present two schemes for driving Raman transitions between the ground state hyperfine manifolds of a single atom trapped within a high-finesse optical cavity. In both schemes, the Raman coupling is generated by standing-wave fields inside the cavity, thus circumventing the optical access limitations that free-space Raman schemes must face in a cavity system. These cavity-based Raman schemes can be used to coherently manipulate both the internal and the motional degrees of freedom of the atom, and thus provide powerful tools for studying cavity quantum electrodynamics. We give a detailed theoretical analysis of each scheme, both for a three-level atom and for a multi-level cesium atom. In addition, we show how these Raman schemes can be used to cool the axial motion of the atom to the quantum ground state, and we perform computer simulations of the cooling process.

quant-ph↗

arXiv2008

Stimulated Raman adiabatic passage in a multi-level atom

We present a general formalism for describing stimulated Raman adiabatic passage in a multi-level atom. The atom is assumed to have two ground state manifolds a and b and an excited state manifold e, and the adiabatic passage is carried out by resonantly driving the a-e and b-e transitions with time-dependent fields. Our formalism gives a complete description of the adiabatic passage process, and can be applied to systems with arbitrary numbers of degenerate states in each manifold and arbitrary couplings of the a-e and b-e transitions. We illustrate the formalism by applying it to both a simple toy model and to adiabatic passage in the Cesium atom.

quant-ph↗

arXiv2007

Optical pumping via incoherent Raman transitions

A new optical pumping scheme is presented that uses incoherent Raman transitions to prepare a trapped Cesium atom in a specific Zeeman state within the 6S_{1/2}, F=3 hyperfine manifold. An important advantage of this scheme over existing optical pumping schemes is that the atom can be prepared in any of the F=3 Zeeman states. We demonstrate the scheme in the context of cavity quantum electrodynamics, but the technique is equally applicable to a wide variety of atomic systems with hyperfine ground-state structure.

quant-ph↗

arXiv2007

Reversible state transfer between light and a single trapped atom

We demonstrate the reversible mapping of a coherent state of light with mean photon number n-bar ~= 1.1 to and from the hyperfine states of an atom trapped within the mode of a high finesse optical cavity. The coherence of the basic processes is verified by mapping the atomic state back onto a field state in a way that depends on the phase of the original coherent state. Our experiment represents an important step towards the realization of cavity QED-based quantum networks, wherein coherent transfer of quantum states enables the distribution of quantum information across the network.

quant-ph↗

arXiv2006

Cooling to the Ground State of Axial Motion for One Atom Strongly Coupled to an Optical Cavity

Localization to the ground state of axial motion is demonstrated for a single, trapped atom strongly coupled to the field of a high finesse optical resonator. The axial atomic motion is cooled by way of coherent Raman transitions on the red vibrational sideband. An efficient state detection scheme enabled by strong coupling in cavity QED is used to record the Raman spectrum, from which the state of atomic motion is inferred. We find that the lowest vibrational level of the axial potential with zero-point energy 13uK is occupied with probability P0~0.95.

quant-ph↗

arXiv2005

Theory of Photon Blockade by an Optical Cavity with One Trapped Atom

In our recent paper [1], we reported observations of photon blockade by one atom strongly coupled to an optical cavity. In support of these measurements, here we provide an expanded discussion of the general phenomenology of photon blockade as well as of the theoretical model and results that were presented in Ref. [1]. We describe the general condition for photon blockade in terms of the transmission coefficients for photon number states. For the atom-cavity system of Ref. [1], we present the model Hamiltonian and examine the relationship of the eigenvalues to the predicted intensity correlation function. We explore the effect of different driving mechanisms on the photon statistics. We also present additional corrections to the model to describe cavity birefringence and ac-Stark shifts. [1] K. M. Birnbaum, A. Boca, R. Miller, A. D. Boozer, T. E. Northup, and H. J. Kimble, Nature 436, 87 (2005).

quant-ph↗

arXiv2004

Observation of the Vacuum-Rabi Spectrum for One Trapped Atom

The transmission spectrum for one atom strongly coupled to the field of a high-finesse optical resonator is observed to exhibit a clearly resolved vacuum-Rabi splitting characteristic of the normal modes in the eigenvalue spectrum of the atom-cavity system. A new Raman scheme for cooling atomic motion along the cavity axis enables a complete spectrum to be recorded for an individual atom trapped within the cavity mode, in contrast to all previous measurements in cavity QED that have required averaging over many atoms.

quant-ph↗

arXiv2004

Comparison of Theory and Experiment for a One-Atom Laser in a Regime of Strong Coupling

Our recent paper reports the experimental realization of a one-atom laser in a regime of strong coupling (Ref. [1]). Here we provide the supporting theoretical analysis relevant to the operating regime of our experiment. By way of a simplified four-state model, we investigate the passage from the domain of conventional laser theory into the regime of strong coupling for a single intracavity atom pumped by coherent external fields. The four-state model is also employed to exhibit the vacuum-Rabi splitting and to calculate the optical spectrum. We next extend this model to incorporate the relevant Zeeman hyperfine states as well as a simple description of the pumping processes in the presence of polarization gradients and atomic motion. This extended model is employed to make quantitative comparisons with the measurements of Ref. [1] for the intracavity photon number versus pump strength and for the photon statistics as expressed by the intensity correlation function g2(tau).

quant-ph↗

arXiv2004

Cavity QED "By The Numbers"

The number of atoms trapped within the mode of an optical cavity is determined in real time by monitoring the transmission of a weak probe beam. Continuous observation of atom number is accomplished in the strong coupling regime of cavity quantum electrodynamics and functions in concert with a cooling scheme for radial atomic motion. The probe transmission exhibits sudden steps from one plateau to the next in response to the time evolution of the intracavity atom number, from N >= 3 to N = 2 to 1 to 0, with some trapping events lasting over 1 second.

quant-ph↗

arXiv2003

A One-Atom Laser in a Regime of Strong Coupling

Although conventional lasers operate with a large number of intracavity atoms, the lasing properties of a single atom in a resonant cavity have been theoretically investigated for more than a decade. Here we report the experimental realization of such a one-atom laser operated in a regime of strong coupling. Our experiment exploits recent advances in cavity quantum electrodynamics that allow one atom to be isolated in an optical cavity in a regime for which one photon is sufficient to saturate the atomic transition. In this regime the observed characteristics of the atom-cavity system are qualitatively different from those of the familiar many atom case. Specifically, we present measurements of intracavity photon number versus pump intensity that exhibit "thresholdless" behavior, and infer that the output flux from the cavity mode exceeds that from atomic fluorescence by more than tenfold. Observations of the second-order intensity correlation function demonstrate that our one-atom laser generates manifestly nonclassical light that exhibits both photon antibunching and sub-Poissonian photon statistics.

quant-ph↗

arXiv2003

Generation of Nonclassical Photon Pairs for Scalable Quantum Communication with Atomic Ensembles

Quantum information science attempts to exploit capabilities from the quantum realm to accomplish tasks that are otherwise impossible in the classical domain [1]. Although sufficient conditions have been formulated for the physical resources required to achieve quantum computation and communication [2], there is an evolving understanding of the power of quantum measurement combined with conditional evolution for accomplishing diverse tasks in quantum information science [3-5]. In this regard, a significant advance is the invention of a protocol by Duan, Lukin, Cirac, and Zoller (DLCZ) [6] for the realization of scalable long distance quantum communication and the distribution of entanglement over quantum networks. Here, we report the first enabling step in the realization of the protocol of DLCZ, namely the observation of quantum correlations for photon pairs generated in the collective emission from an atomic ensemble. The nonclassical character of the fields is evidenced by the violation of a Cauchy-Schwarz inequality for the two fields (1,2). As compared to prior investigations of nonclassical correlations for photon pairs produced in atomic cascades [7] and in parametric down conversion [8], our experiment is distinct in that the correlated (1,2) photons are separated by a programmable time interval delta t, with delta t ~ 400 nsec in our initial experiments.

quant-ph↗

arXiv2003

State-Insensitive Cooling and Trapping of Single Atoms in an Optical Cavity

Single Cesium atoms are cooled and trapped inside a small optical cavity by way of a novel far-off-resonance dipole-force trap (FORT), with observed lifetimes of 2 to 3 seconds. Trapped atoms are observed continuously via transmission of a strongly coupled probe beam, with individual events lasting ~ 1 s. The loss of successive atoms from the trap N = 3 -> 2 -> 1 -> 0 is thereby monitored in real time. Trapping, cooling, and interactions with strong coupling are enabled by the FORT potential, for which the center-of-mass motion is only weakly dependent on the atom's internal state.

quant-ph↗