Adam Stokes

Quantum-enhanced metrology with the single-mode coherent states of an optical cavity inside a quantum feedback loop

In this paper, we use the nonlinear generator of dynamics of the individual quantum trajectories of an optical cavity inside an instantaneous quantum feedback loop to measure the phase shift between two pathways of light with a precision above the standard quantum limit. The feedback laser provides a reference frame and constantly increases the dependence of the state of the resonator on the unknown phase. Since our quantum metrology scheme can be implemented with current technology and does not require highly efficient single photon detectors, it should be of practical interest until highly entangled many-photon states become more readily available.

On the gauge of the natural lineshape

We use a general formulation of non-relativistic quantum electrodynamics in which the gauge freedom is carried by the arbitrary transverse component of the Green?s function for the divergence operator to calculate the natural lineshape of spontaneous emission, thus discerning the full dependence of the result on the choice of gauge. We also use a representation of the Hamiltonian in which the virtual field associated with the atomic ground state is explicitly absent. We consider two processes by which the atom is excited; the first is resonant absorption of incident radiation with a sharp line. This treatment is then adapted to derive a resonance fluorescence rate associated with the Lamb line in atomic hydrogen. Second we consider the atom?s excitation due to irradiation with a laser pulse treated semi-classically. An experiment could be used to reveal which of the calculated lineshape distributions is closest to the measured one. This would provide an answer to a question of fundamental importance; how does one best describe atom?radiation interactions with the canonical formalism?

The Casimir effect for fields with arbitrary spin

The Casimir force between two perfectly reflecting parallel plates is considered. In a recent paper we presented generalised physical boundary conditions describing perfectly reflecting parallel plates. These boundary conditions are applicable to a field possessing any spin, and include the well-known spin-1/2 and spin-1 boundary conditions as special cases. Here we use these general boundary conditions to show that the allowed values of energy-momentum turn out to be the same for any massless fermionic field and the same for any massless bosonic field. As a result one expects to obtain only two possible Casimir forces, one associated with fermions and the other with bosons. We explicitly verify that this is the case for the fields up to spin-2. A significant implication of our work is that periodic boundary conditions cannot be applied to a fermionic field confined between two parallel plates.

A master equation for strongly interacting dipoles

We consider a pair of dipoles for which direct electrostatic dipole-dipole interactions may be significantly larger than the coupling to transverse radiation. We derive a master equation using the Coulomb gauge, which naturally enables us to include the inter-dipole Coulomb energy within the system Hamiltonian rather than the interaction. In contrast, the standard master equation for a two- dipole system, which depends entirely on well-known gauge-invariant S-matrix elements, is usually derived using the multipolar gauge, wherein there is no explicit inter-dipole Coulomb interaction. We show using a generalised arbitrary-gauge light-matter Hamiltonian that this master equation is obtained in other gauges only if the inter-dipole Coulomb interaction is kept within the interaction Hamiltonian rather than the unperturbed part as in our derivation. Thus, our master equation, while still gauge-invariant, depends on different S-matrix elements, which give separation-dependent corrections to the standard matrix elements describing resonant energy transfer and collective decay. The two master equations coincide in the large separation limit where static couplings are negligible. We provide an application of our master equation by finding separation-dependent corrections to the natural emission spectrum of the two-dipole system.

Quantum-enhanced Metrology without Entanglement based on Optical Cavities with Feedback

There are a number of different strategies to measure the phase shift between two pathways of light more efficiently than suggested by the standard quantum limit. One way is to use highly entangled photons. Another way is to expose photons to a non-linear or interacting Hamiltonian. This paper emphasises that the conditional dynamics of open quantum systems provides an interesting additional tool for quantum-enhanced metrology. As a concrete example, we review a recent scheme which exploits the conditional dynamics of a laser-driven optical cavity with spontaneous photon emission inside a quantum feedback loop. Deducing information from second-order photon correlation measurements requires neither optical non-linearities nor entangled photons and should therefore be of immediate practical interest.

Using thermodynamics to identify quantum subsystems

There are many ways to decompose the Hilbert space of a composite quantum system into tensor product subspaces. Different subsystem decompositions generally imply different interaction Hamiltonians V, and therefore different expectation values for subsystem observables. This means that the uniqueness of physical predictions is not guaranteed, despite the uniqueness of the total Hamiltonian H and the total Hilbert space . Here we use Clausius’ version of the second law of thermodynamics (CSL) and standard identifications of thermodynamic quantities to identify possible subsystem decompositions. It is shown that agreement with the CSL is obtained, whenever the total Hamiltonian and the subsystem-dependent interaction Hamiltonian commute (i.e. ). Not imposing this constraint can result in the transfer of heat from a cooler to a hotter subsystem, in conflict with thermodynamics. We also investigate the status of the CSL with respect to non-standard definitions of thermodynamic quantities and quantum subsystems.

A generalized bag-like boundary condition for fields with arbitrary spin

Boundary conditions (BCs) for the Maxwell and Dirac fields at material surfaces are widely-used and physically well-motivated, but do not appear to have been generalized to deal with higher spin fields. As a result there is no clear prescription as to which BCs should be selected in order to obtain physically-relevant results pertaining to confined higher spin fields. This lack of understanding is significant given that boundary-dependent phenomena are ubiquitous across physics, a prominent example being the Casimir effect. Here, we use the two-spinor calculus formalism to present a unified treatment of BCs routinely employed in the treatment of spin- and spin-1 fields. We then use this unification to obtain a BC that can be applied to massless fields of any spin, including the spin-2 graviton, and its supersymmetric partner the spin- gravitino.

An alternative electric-field spectrum for laser-driven atomic systems

We adopt an open quantum systems perspective to calculate the power spectrum associated with the electric field generated by an atomic dipole moment undergoing resonant laser-driving. This spectrum has a similar shape to the usual Mollow spectrum, but also has some distinct features. For sufficiently strong laser driving, both spectra have a symmetric triplet structure with a large central peak and two sidebands. However, the relative height of the sidebands to the central peak differs in each case. The two spectra also behave quite differently when the laser Rabi frequency is varied. Both spectra may be of interest in high-precision experiments into the quantum physics of atomic systems, especially artificial atoms.

Composite Quantum Systems and Environment‐Induced Heating

In recent years, much attention has been paid to the development of techniques which transfer trapped particles to very low temperatures. Here we focus our attention on a heating mechanism which contributes to the finite temperature limit in laser sideband cooling experiments with trapped ions. It is emphasized that similar heating processes might be present in a variety of composite quantum systems whose components couple individually to different environments. For example, quantum optical heating effects might contribute significantly to the very high temperatures which occur during the collapse phase in sonoluminescence experiments. It might even be possible to design composite quantum systems, like atom‐cavity systems, such that they continuously emit photons even in the absence of external driving.