Completeness for coherent states in a magnetic-solenoid field

This paper completes our study of coherent states in the so-called magnetic-solenoid field (a collinear combination of a constant uniform magnetic field and Aharonov-Bohm solenoid field) presented in Bagrov et al (2010 J. Phys. A: Math. Theor. 43 354016, 2011 J. Phys. A: Math. Theor. 44 055301). Here, we succeeded in proving nontrivial completeness relations for non-relativistic and relativistic coherent states in such a field. In addition, we solve here the relevant Stieltjes moment problem and present a comparative analysis of our coherent states and the well-known, in the case of pure uniform magnetic field, Malkin-Man'ko coherent states.

Coherent states and related quantizations for unbounded motions

We discuss the construction of coherent states (CS) for systems with continuous spectra. First, we propose to adopt the Malkin-Manko approach, developed for systems with discrete spectra, to the case under consideration. Following this approach, we consider two examples, a free particle and a particle in a linear potential. Second, we generalize the approach of action-angle CS to systems with continuous spectra. In the first approach we start with a well-defined quantum formulation (canonical quantization) of a physical system and the construction of CS follows from such a quantization. In the second approach, the quantization procedure is inherent to the CS construction itself.

Spin coherent states in NMR quadrupolar system: experimental and theoretical applications

Working with nuclear magnetic resonance (NMR) in quadrupolar spin systems, in this paper we transfer the concept of atomic coherent state to the nuclear spin context, where it is referred to as pseudonuclear spin coherent state (pseudo-NSCS). Experimentally, we discuss the initialization of the pseudo- NSCSs and also their quantum control, implemented by polar and azimuthal rotations. Theoretically, we compute the geometric phases acquired by an initial pseudo-NSCS on undergoing three distinct cyclic evolutions: (i) the free evolution of the NMR quadrupolar system and, by analogy with the evolution of the NMR quadrupolar system, that of (ii) single-mode and (iii) two-mode Bose-Einstein Condensate like system. By means of these analogies, we derive, through spin angular momentum operators, results equivalent to those presented in the literature for orbital angular momentum operators. The pseudo-NSCS description is a starting point to introduce the spin squeezed state and quantum metrology into nuclear spin systems of liquid crystal or solid matter.

Towards higher precision and operational use of optical homodyne tomograms

We present the results of an operational use of experimentally measured optical tomograms to determine state characteristics (purity) avoiding any reconstruction of quasiprobabilities. We also develop a natural way how to estimate the errors (including both statistical and systematic ones) by an analysis of the experimental data themselves. Precision of the experiment can be increased by postselecting the data with minimal (systematic) errors. We demonstrate those techniques by considering coherent and photon-added coherent states measured via the time-domain improved homodyne detection. The operational use and precision of the data allowed us to check purity-dependent uncertainty relations and uncertainty relations for Shannon and Renyi entropies.

Spin coherence generation in negatively charged self-assembled (In,Ga)As quantum dots by pumping excited trion states

Spin coherence generation in an ensemble of negatively charged (In,Ga)As/GaAs quantum dots was investigated by picosecond time-resolved pump-probe spectroscopy measuring ellipticity. Robust coherence of the ground-state electron spins is generated by pumping excited charged exciton (trion) states. The phase of the coherent state, as evidenced by the spin ensemble precession about an external magnetic field, varies relative to spin coherence generation resonant with the ground state. The phase variation depends on the pump photon energy. It is determined by (a) pumping dominantly either singlet or triplet excited states, leading to a phase inversion, and (b) the subsequent carrier relaxation into the ground states. From the dependence of the precession phase and the measured g factors, information about the quantum dot shell splitting and the exchange energy splitting between triplet and singlet states can be extracted in the ensemble.

Magneto-optical probe of quantum Hall states in a wide parabolic well modulated by random potential

Polarized photoluminescence from weakly coupled random multiple well quasi-three-dimensional electron system is studied in the regime of the integer quantum Hall effect. Two quantum Hall ferromagnetic ground states assigned to the uncorrelated miniband quantum Hall state and to the spontaneous interwell phase coherent dimer quantum Hall state are observed. Photoluminescence associated with these states exhibits features caused by finite-size skyrmions: dramatic reduction of the electron spin polarization when the magnetic field is increased past the filling factor nu = 1. The effective skyrmion size is larger than in two-dimensional electron systems.