New strategies for phase estimation in quantum optics

Sufficient conditions for a quantum dynamical semigroup (QDS) to be unital are proved for a class of problems in quantum optics with Hamiltonians which are self-adjoint polynomials of any finite order in creation and annihilation operators. The order of the Hamiltonian may be higher than the order of completely positive part of the formal generator of a QDS.

At the Institute of Optics, University of Rochester (UR), we have adapted to the main challenge (the lack of space in the curriculum) by developing a series of modular 3-hour experiments and 20-min-demonstrations based on technical elective, 4-credit-hour laboratory course “Quantum Optics and Nano-Optics Laboratory” (OPT 253/OPT453/PHY434), that were incorporated into a number of required courses ranging from freshman to senior level. Rochester Monroe Community College (MCC) students also benefited from this facility that was supported by four NSF grants. MCC students carried out two 3-hour labs on photon quantum mechanics at the UR. Since 2006, total 566 students passed through the labs with lab reports submission (including 144 MCC students) and more than 250 students through lab demonstrations. In basic class OPT 253, four teaching labs were prepared on generation and characterization of entangled and single (antibunched) photons demonstrating the laws of quantum mechanics: (1) entanglement and Bell’s inequalities, (2) single-photon interference (Young’s double slit experiment and Mach-Zehnder interferometer), (3) confocal microscope imaging of single-emitter (colloidal nanocrystal quantum dots and NV-center nanodiamonds) fluorescence within photonic (liquid crystal photonic bandgap microcavities) or plasmonic (gold bowtie nanoantennas) nanostructures, (4) Hanbury Brown and Twiss setup. Fluorescence antibunching from nanoemitters. Students also carried out measurements of nanodiamond topography using atomic force microscopy and prepared photonic bandgap materials from cholesteric liquid crystals. Manuals, student reports, presentations, lecture materials and quizzes, as well as some NSF grants’ reports are placed on a website http://www.optics.rochester.edu/workgroups/lukishova/QuantumOpticsLab/. In 2011 UR hosted 6 professors from different US universities in three-days training of these experiments participating in the Immersion Program of the Advanced Laboratory Physics Association.

We investigate the phase sensitivity of the SU(1,1) interfereometer [SU(1,1)I] and the modified Mach–Zehnder interferometer (MMZI) with the entangled coherent states (ECS) as inputs. We consider the ideal case and the situations in which the photon losses are taken into account. We find that, under ideal conditions, the phase sensitivity of both the MMZI and the SU(1,1)I can beat the shot-noise limit (SNL) and approach the Heisenberg limit (HL). In the presence of photon losses, the ECS can beat the coherent and squeezed states as inputs in the SU(1,1)I, and the MMZI is more robust against internal photon losses than the SU(1,1)I.

Exotic looped trajectories via quantum marking

Quantum-mechanical wave-particle duality is quantified in terms of a trade-off relation between the fringe visibility and the which-way distinguishability in an interference experiment. This relation was recently generalized by Banaszek et al. [Nat. Commun. 4, 2594 (2013)] when the particle is equipped with an internal degree of freedom such as spin. Here, we extend the visibility-distinguishability trade-off relation to quantum interference of a particle possessing an internal degree of freedom, when the which-way detector state is entangled with an ancillary system. We introduce an extended which-way distinguishability ${\mathcal{D}}_{E}$ and the associated extended fringe visibility ${\mathcal{V}}_{E}$, satisfying the inequality ${\mathcal{D}}_{E}^{2}+{\mathcal{V}}_{E}^{2}\ensuremath{\le}1$ in this scenario. We illustrate, with the help of three specific examples, that while the which-way information inferred solely from the detector state (without ancilla) vanishes, the extended distinguishability retrievable via measurements on the detector-ancilla entangled state is nonzero. Furthermore, in all the three examples, the extended visibility and the generalized visibility (which was introduced by Banaszek et al.) match identically with each other.

In many problems in quantum optics, damping plays an important role. These include, for example, the decay of an atom in an excited state to a lower state and the decay of the radiation field inside a cavity with partially transparent mirrors. In general, damping of a system is described by its interaction with a reservoir with a large number of degrees of freedom. We are interested, however, in the evolution of the variables associated with the system only. This requires us to obtain the equations of motion for the system of interest only after tracing over the reservoir variables. There are several different approaches to deal with this problem.

We derive the generalized set of Maxwell-Bloch equations which takes into account the dependence of relaxation coefficients on the amplitude and frequency of the coherent field. This has interesting implications in many problems in quantum optics and laser physics, e.g., the problem of lasing without inversion due to a strong coherent generating field.

We discuss the classical and quantum mechanical evolution of systems described by a Hamiltonian that is a function of a solvable one, both classically and quantum mechanically. The case in which the solvable Hamiltonian corresponds to the harmonic oscillator is emphasized. We show that, in spite of the similarities at the classical level, the quantum evolution is very different. In particular, this difference is important in constructing coherent states, which is impossible in most cases. The class of Hamiltonians we consider is interesting due to its pedagogical value and its applicability to some open research problems in quantum optics and quantum gravity.

One of the long-standing problems in quantum optics and laser physics is the observation of both equilibrium and non-equilibrium (Dicke) superradiant states in two-level (qubit) systems interacting with the quantized electromagnetic (EM) field. We demonstrate that the superradiant phase transition (PT) at thermal equilibrium in such a system is close to ultrastrong light–matter coupling (USC) condition, which is currently available for superconducting devices. We examine the USC regime for EM fields interacting with two-level systems located in highly connected graph nodes of photonic networks beyond the rotating wave approximation. We find that a critical matter–field coupling parameter reduces ⟨ k ⟩ times due to network peculiarities providing suitable conditions for equilibrium PT observation; ⟨ k ⟩ is a network average node degree. We study the non-equilibrium (Dicke) superradiance for the same network system and show that superradiance appears as a non-equilibrium PT to the superradiant laser operating within a bad cavity limit. We show that population inversion in this case plays the same role as the reciprocal temperature inherent to the equilibrium superradiant PT. Our results open new perspectives for experimental observation of superradiance in cavity-free systems in the gigahertz photonic regime and beyond.

Quantum statistical properties of interacting optical fields in Kerr nonlinear coupler can be regarded as one of the most fundamental problems in quantum optics. As the analytical solution to these systems is not always possible, a semi-analytic or direct numerical solution has to be employed to obtain more complete description of their evolution. This paper investigates the quantum properties of a four-mode coupler composed of two Kerr nonlinear waveguides via phase-space representation. In this system, the electromagnetic field is described by its Hamiltonian and the time evolution of the system is described by Von-Neumann equation. Following the standard techniques, the master equation for the density matrix of the system is obtained and converted to the corresponding classical Fokker-Planck equation using both positive-P and Wigner representations. The corresponding set of Langevin Stochastic equations are then obtained from the Fokker-Planck equation using Ito rules. Finally, the system is integrated numerically and averaged over many trajectories to get the relevant information. The dynamics of the mean fields, the effects of self-action nonlinearity, cross-action coupling and initial energy of the coherent light on the evolution of the field quadrature variances are investigated. Further, the influences of multimode interaction on the dynamics of the squeezed states are discussed. We show that the system can produce squeezed states in both quadrature variances for all calculated parameters. In addition, the multimode interaction extends the range of squeezing at the expense of its amplitude.

This is a set of lecture notes given by the authors at the Universities of Rochester, Arkansas and Puerto Rico. This volume introduces the main ideas of chaos and its applications to a broad range of problems in quantum optics, electronics and laser physics. Contents: Introduction; Nonlinearity; The Period Doubling Route to Chaos; The Duffing Oscillator; Strange Attractors; Two-Frequency Route to Chaos; Intermittency; Dimensions of Attractors; Noise, The Lorenz Model and the Single-Mode Laser; Chaotic Lasers: Theory and Experiment; Hamiltonian Systems; The Henon-Heiles System; The Standard Mapping; Fat Fractals; Ergodicity and Mixing; Chaos and the Microwave Ionization of Hydrogen; The Kicked Pendulum: Classical Theory and Quantum Theory; Chaos and Multiple-Photon Excitation of Molecular Vibrations; Chaos and Molecular Rotations; Ideas in Quantum Chaos; Outlook.

Conditions sufficient for a minimal quantum dynamical semigroup (QDS) to be conservative are proved for the class of problems in quantum optics under the assumption that the self-adjoint Hamiltonian of the QDS is a finite degree polynomial in the creation and annihilation operators. The degree of the Hamiltonian may be greater than the degree of the completely positive part of the generator of the QDS. The conservativity (or the unital property) of a minimal QDS implies the uniqueness of the solution of the corresponding master Markov equation, i.e., in the unital case, the formal generator determines the QDS uniquely; moreover, in the Heisenberg representation, the QDS preserves the unit observable, and in the Schrodinger representation, it preserves the trace of the initial state. The analogs of the conservativity condition for classical Markov evolution equations (such as the heat and the Kolmogorov--Feller equations) are known as nonexplosion conditions or conditions excluding the escape of trajectories to infinity.

Atom Interferometry and the Quantum Theory of Measurement

Get PDF Email Share Share with Facebook Tweet This Post on reddit Share with LinkedIn Add to CiteULike Add to Mendeley Add to BibSonomy Get Citation Copy Citation Text M. Napolitano, M. Koschorreck, B. Dubost, N. Behbood, R.J. Sewell, and M.W. Mitchell, "Quantum Optics and the “Heisenberg Limit” of Measurement," Optics & Photonics News 22(12), 40-40 (2011) Export Citation BibTex Endnote (RIS) HTML Plain Text Citation alert Save article

De Broglie proposed the matter wave in 1924. The de Broglie wave is neither a mechanical wave nor an electromagnetic wave and has a very short wavelength. The Davisson-Germer electron diffraction experiment performed in 1925 involved bombarding the surface of a nickel crystal with a narrow beam of electrons. When the accelerating voltage V was maintained at 54 V, the wavelength of the incident electron was λ=h/ <mml:math display="inline"> <mml:msqrt> <mml:mn>2</mml:mn> <mml:mi mathvariant="normal">m</mml:mi> <mml:mi mathvariant="normal">e</mml:mi> <mml:mi mathvariant="normal">V</mml:mi> </mml:msqrt> </mml:math> = 0.167 nm [Y. S. Chen and Z. Z. Li, College Physics (Tianjin University, Tianjin, 1999)] demonstrating the existence of the matter wave. We introduce a type of electron wave with a very long wavelength in this study that is different from the matter wave. For example, the wavelength of the electron wave can reach 0.43 mm in the double-slit interference of electrons. Experiments demonstrate that this long-wavelength electron wave can produce both double-slit interference and electron diffraction. A comparative analysis of matter and electron waves reveals the physical natures of these waves and wave‐particle duality.