Quantum trajectories for propagating Fock states

We derive quantum trajectories (also known as stochastic master equations) that describe an arbitrary quantum system probed by a propagating wave packet of light prepared in a continuous-mode Fock state. We consider three detection schemes of the output light: photon counting, homodyne detection, and heterodyne detection. We generalize to input field states that are superpositions and or mixtures of Fock states and illustrate the formalism with several examples.Comment: 20 pages, 4 figure

Open Systems Dynamics for Propagating Quantum Fields

In this dissertation, I explore interactions between matter and propagating light. The electromagnetic field is modeled as a reservoir of quantum harmonic oscillators successively streaming past a quantum system. Each weak and fleeting interaction entangles the light and the system, and the light continues its course. Within the framework of open quantum systems, the light is eventually traced out, leaving the reduced quantum state of the system as the primary mathematical subject. Two major results are presented. The first is a master equation approach for a quantum system interacting with a traveling wave packet prepared with a definite number of photons. In contrast to quasi-classical states, such as coherent or thermal fields, these N-photon states possess temporal mode entanglement, and local interactions in time have nonlocal consequences. The second is a model for a three-dimensional light-matter interface for an atomic ensemble interacting with a paraxial laser beam and its application to the generation of QND spin squeezing. Both coherent and incoherent dynamics due to spatially inhomogeneous atom-light coupling across the ensemble are accounted for. Measurement of paraxially scattered light can generate squeezing of an atomic spin wave, while diffusely scattered photons lead to spatially local decoherence.Comment: PhD thesis. 261 page

Collective Uncertainty in Partially-Polarized and Partially-Decohered Spin-1/2 Systems

It has become common practice to model large spin ensembles as an effective pseudospin with total angular momentum J = N x j, where j is the spin per particle. Such approaches (at least implicitly) restrict the quantum state of the ensemble to the so-called symmetric Hilbert space. Here, we argue that symmetric states are not generally well-preserved under the type of decoherence typical of experiments involving large clouds of atoms or ions. In particular, symmetric states are rapidly degraded under models of decoherence that act identically but locally on the different members of the ensemble. Using an approach [Phys. Rev. A 78, 052101 (2008)] that is not limited to the symmetric Hilbert space, we explore potential pitfalls in the design and interpretation of experiments on spin-squeezing and collective atomic phenomena when the properties of the symmetric states are extended to systems where they do not apply.Comment: 13 pages, 7 figure

Dispersive response of atoms trapped near the surface of an optical nanofiber with applications to quantum nondemolition measurement and spin squeezing

We study the strong coupling between photons and atoms that can be achieved in an optical nanofiber geometry when the interaction is dispersive. While the Purcell enhancement factor for spontaneous emission into the guided mode does not reach the strong-coupling regime for individual atoms, one can obtain high cooperativity for ensembles of a few thousand atoms due to the tight confinement of the guided modes and constructive interference over the entire chain of trapped atoms. We calculate the dyadic Green's function, which determines the scattering of light by atoms in the presence of the fiber, and thus the phase shift and polarization rotation induced on the guided light by the trapped atoms. The Green's function is related to a full Heisenberg-Langevin treatment of the dispersive response of the quantized field to tensor polarizable atoms. We apply our formalism to quantum nondemolition (QND) measurement of the atoms via polarimetry. We study shot-noise-limited detection of atom number for atoms in a completely mixed spin state and the squeezing of projection noise for atoms in clock states. Compared with squeezing of atomic ensembles in free space, we capitalize on unique features that arise in the nanofiber geometry including anisotropy of both the intensity and polarization of the guided modes. We use a first principles stochastic master equation to model the squeezing as function of time in the presence of decoherence due to optical pumping. We find a peak metrological squeezing of ~5 dB is achievable with current technology for ~2500 atoms trapped 180 nm from the surface of a nanofiber with radius a=225 nm.Comment: To be appeared on PR

Collisional-model quantum trajectories for entangled qubit environments

We study the dynamics of quantum systems interacting with a stream of entangled qubits. Under fairly general conditions, we present a detailed framework describing the conditional dynamical maps for the system, called quantum trajectories, when the qubits are measured. Depending on the measurement basis, these quantum trajectories can be jump-type or diffusive-type, and they can exhibit features not present with quantum optical and single-qubit trajectories. As an example, we consider the case of two remote atoms, where jump-type quantum trajectories herald the birth and death of entanglement.Comment: 25 pages, 6 figure

Encoding qubits into oscillators with atomic ensembles and squeezed light

The Gottesman-Kitaev-Preskill (GKP) encoding of a qubit within an oscillator provides a number of advantages when used in a fault-tolerant architecture for quantum computing, most notably that Gaussian operations suffice to implement all single- and two-qubit Clifford gates. The main drawback of the encoding is that the logical states themselves are challenging to produce. Here we present a method for generating optical GKP-encoded qubits by coupling an atomic ensemble to a squeezed state of light. Particular outcomes of a subsequent spin measurement of the ensemble herald successful generation of the resource state in the optical mode. We analyze the method in terms of the resources required (total spin and amount of squeezing) and the probability of success. We propose a physical implementation using a Faraday-based quantum non-demolition interaction.Comment: (v2) consistent with published version; (v1) 16 pages, 5 figure