Joel F. Corney

Quantum noise in optical fibers I: stochastic equations

We analyze the quantum dynamics of radiation propagating in a single-mode optical fiber with dispersion, nonlinearity, and Raman coupling to thermal phonons. We start from a fundamental Hamiltonian that includes the principal known nonlinear effects and quantum-noise sources, including linear gain and loss. Both Markovian and frequency-dependent, non-Markovian reservoirs are treated. This treatment allows quantum Langevin equations, which have a classical form except for additional quantum-noise terms, to be calculated. In practical calculations, it is more useful to transform to Wigner or +P quasi-probability operator representations. These transformations result in stochastic equations that can be analyzed by use of perturbation theory or exact numerical techniques. The results have applications to fiber-optics communications, networking, and sensor technology.

Quantum optical waveform conversion.

Proposals for long-distance quantum communication rely on the entanglement of matter-based quantum nodes through optical communications channels, but the entangling light pulses have poor temporal behavior in current experiments. Here we show that nonlinear mixing of a quantum light pulse with a spectrally tailored classical field can compress the quantum pulse by more than a factor of 100 and flexibly reshape its temporal waveform while preserving all quantum properties, including entanglement. Our scheme paves the way for quantum communication at the full data rate of optical telecommunications.

Gaussian Quantum Monte Carlo Methods for Fermions and Bosons

We introduce a new class of quantum Monte Carlo methods, based on a Gaussian quantum operator representation of fermionic states. The methods enable first-principles dynamical or equilibrium calculations in many-body Fermi systems, and, combined with the existing Gaussian representation for bosons, provide a unified method of simulating Bose-Fermi systems. As an application relevant to the Fermi sign problem, we calculate finite-temperature properties of the two dimensional Hubbard model and the dynamics in a simple model of coherent molecular dissociation.

Experimental evidence for Raman-induced limits to efficient squeezing in optical fibers

We report new experiments on polarization squeezing using ultrashort photonic pulses in a single pass of a birefringent fiber. We measure what is to our knowledge a record squeezing of -6.8+/-0.3 dB in optical fibers, which when corrected for linear losses is -10.4+/-0.8 dB. The measured polarization squeezing as a function of optical pulse energy, which spans a wide range from 3.5-178.8 pJ, shows a very good agreement with the quantum simulations, and for the first time we see the proof experimentally that Raman effects limit and reduce squeezing at high pulse energy.

Many-body quantum dynamics of polarization squeezing in optical fibers

We report new experiments that test quantum dynamical predictions of polarization squeezing for ultrashort photonic pulses in a birefringent fiber, including all relevant dissipative effects. This exponentially complex many-body problem is solved by means of a stochastic phase-space method. The squeezing is calculated and compared to experimental data, resulting in excellent quantitative agreement. From the simulations, we identify the physical limits to quantum noise reduction in optical fibers. The research represents a significant experimental test of first-principles time-domain quantum dynamics in a one-dimensional interacting Bose gas coupled to dissipative reservoirs.

Gaussian phase-space representations for fermions

We introduce a positive phase-space representation for fermions, using the most general possible multimode Gaussian operator basis. The representation generalizes previous bosonic quantum phase-space methods to Fermi systems. We derive equivalences between quantum and stochastic moments, as well as operator correspondences that map quantum operator evolution onto stochastic processes in phase space. The representation thus enables first-principles quantum dynamical or equilibrium calculations in many-body Fermi systems. Potential applications are to strongly interacting and correlated Fermi gases, including coherent behavior in open systems and nanostructures described by master equations. Examples of an ideal gas and the Hubbard model are given, as well as a generic open system, in order to illustrate these ideas.

Modulational instability in periodic quadratic nonlinear materials.

We investigate the modulational instability of plane waves in quadratic nonlinear materials with linear and nonlinear quasi-phase-matching gratings. Exact Floquet calculations, confirmed by numerical simulations, show that the periodicity can drastically alter the gain spectrum but never completely removes the instability. The low-frequency part of the gain spectrum is accurately predicted by an averaged theory and disappears for certain gratings. The high-frequency part is related to the inherent gain of the homogeneous non-phase-matched material and is a consistent spectral feature.

Quantum dynamics of evaporatively cooled Bose-Einstein condensates

We report on dynamical simulations of Bose-Einstein condensation via evaporative cooling in an atomic trap. The results show evidence for spontaneous vortex formation and quantum dynamics in small traps. [S1050-2947(99)50110-8].

Gaussian quantum operator representation for bosons

We introduce a Gaussian quantum operator representation, using the most general possible multimode Gaussian operator basis. The representation unifies and substantially extends existing phase-space representations of density matrices for Bose systems and also includes generalized squeezed-state and thermal bases. It enables first-principles dynamical or equilibrium calculations in quantum many-body systems, with quantum uncertainties appearing as dynamical objects. Any quadratic Liouville equation for the density operator results in a purely deterministic time evolution. Any cubic or quartic master equation can be treated using stochastic methods.

Quantum noise in optical fibers II: Raman jitter in soliton communications

The dynamics of a soliton propagating in a single-mode optical fiber with gain, loss, and Raman coupling to thermal phonons is analyzed. Using both soliton perturbation theory and exact numerical techniques, we propose that intrinsic thermal quantum noise from the phonon reservoirs is a larger source of jitter and other perturbations than the gain-related Gordon–Haus noise for short pulses (≲1 ps), assuming typical fiber parameters. The size of the Raman timing jitter is evaluated for both bright and dark (topological) solitons and is larger for bright solitons. Because Raman thermal quantum noise is a nonlinear, multiplicative noise source, these effects are stronger for the more intense pulses that are needed to propagate as solitons in the short-pulse regime. Thus Raman noise may place additional limitations on fiber-optical communications and networking by use of ultrafast (subpicosecond) pulses.