arXiv subjects

A. Vourdas

Publications and source records attributed to A. Vourdas.

At least 55 records · Page 3Linked to original sources

arXiv2012

Weak mutually unbiased bases

Quantum systems with variables in ${\mathbb Z}(d)$ are considered. The properties of lines in the ${\mathbb Z}(d)\times {\mathbb Z}(d)$ phase space of these systems, are studied. Weak mutually unbiased bases in these systems are defined as bases for which the overlap of any two vectors in two different bases, is equal to $d^{-1/2}$ or alternatively to one of the $d_i^{-1/2},0$ (where $d_i$ is a divisor of $d$ apart from $d,1$). They are designed for the geometry of the ${\mathbb Z}(d)\times {\mathbb Z}(d)$ phase space, in the sense that there is a duality between the weak mutually unbiased bases and the maximal lines through the origin. In the special case of prime $d$, there are no divisors of $d$ apart from $1,d$ and the weak mutually unbiased bases are mutually unbiased bases.

quant-ph↗

arXiv2012

Generalized Bargmann functions, their growth and von Neumann lattices

Generalized Bargmann representations which are based on generalized coherent states are considered. The growth of the corresponding analytic functions in the complex plane is studied. Results about the overcompleteness or undercompleteness of discrete sets of these generalized coherent states are given. Several examples are discussed in detail.

quant-ph↗

arXiv2006

Harmonic analysis on a galois field and its subfields

Complex functions $χ(m)$ where $m$ belongs to a Galois field $GF(p^ \ell)$, are considered. Fourier transforms, displacements in the $GF(p^ \ell) \times GF(p^ \ell)$ phase space and symplectic $Sp(2,GF(p^ \ell))$ transforms of these functions are studied. It is shown that the formalism inherits many features from the theory of Galois fields. For example, Frobenius transformations are defined which leave fixed all functions $h(n)$ where $n$ belongs to a subfield $GF(p^ d)$ of the $GF(p^ \ell)$. The relationship between harmonic analysis (or quantum mechanics) on $GF(p^ \ell)$ and harmonic analysis on its subfields, is studied.

math-ph↗

arXiv2006

The Frobenius formalism in Galois quantum systems

Quantum systems in which the position and momentum take values in the ring ${\cal Z}_d$ and which are described with $d$-dimensional Hilbert space, are considered. When $d$ is the power of a prime, the position and momentum take values in the Galois field $GF(p^ \ell)$, the position-momentum phase space is a finite geometry and the corresponding `Galois quantum systems' have stronger properties. The study of these systems uses ideas from the subject of field extension in the context of quantum mechanics. The Frobenius automorphism in Galois fields leads to Frobenius subspaces and Frobenius transformations in Galois quantum systems. Links between the Frobenius formalism and Riemann surfaces, are discussed.

quant-ph↗

arXiv2005

Phase space methods for particles on a circle

The phase space $S\times Z$ for a particle on a circle is considered. Displacement operators in this phase space are introduced and their properties are studied. Wigner and Weyl functions in this context are also considered and their physical interpretation and properties are discussed. All results are compared and contrasted with the corresponding ones for the harmonic oscillator in the $R \times R$ phase space.

quant-ph↗

arXiv2005

Analytic Representation of Finite Quantum Systems

A transform between functions in R and functions in Zd is used to define the analogue of number and coherent states in the context of finite d-dimensional quantum systems. The coherent states are used to define an analytic representation in terms of theta functions. All states are represented by entire functions with growth of order 2, which have exactly d zeros in each cell. The analytic function of a state is constructed from its zeros. Results about the completeness of finite sets of coherent states within a cell are derived.

quant-ph↗

arXiv2005

Electron interference in mesoscopic devices in the presence of nonclassical electromagnetic fields

The interaction of mesoscopic interference devices with nonclassical electromagnetic fields is studied. The external quantum fields induce a phase factor on the electric charges. This phase factor, which is a generalization of the standard Aharonov-Bohm phase factor, is in the case of nonclassical electromagnetic fields a quantum mechanical operator. Its expectation value depends on the density matrix describing the nonclassical photons and determines the interference. Several examples are discussed, which show that the quantum noise of the nonclassical photons destroys slightly the electron interference fringes. An interesting application arises in the context of distant electron interference devices, irradiated with entangled photons. In this case the interfering electrons in the two devices become entangled. The same ideas are applied in the context of SQUID rings irradiated with nonclassical electromagnetic fields. It is shown that the statistics of the Cooper pairs tunneling through the Josephson junction depend on the statistics of the photons.

quant-ph↗

arXiv2004

Entangled quantum currents in distant mesoscopic Josephson junctions

Two mesoscopic SQUID rings which are far from each other, are considered. A source of two-mode nonclassical microwaves irradiates the two rings with correlated photons. The Josephson currents are in this case quantum mechanical operators, and their expectation values with respect to the density matrix of the microwaves, yield the experimentally observed currents. Classically correlated (separable) and quantum mechanically correlated (entangled) microwaves are considered, and their effect on the Josephson currents is quantified. Results for two different examples that involve microwaves in number states and coherent states are derived. It is shown that the quantum statistics of the tunnelling electron pairs through the Josephson junctions in the two rings, are correlated.

cond-mat.supr-con↗

arXiv2004

Quantum Statistics and Entanglement of Two Electromagnetic Field Modes Coupled via a Mesoscopic SQUID Ring

In this paper we investigate the behaviour of a fully quantum mechanical system consisting of a mesoscopic SQUID ring coupled to one or two electromagnetic field modes. We show that we can use a static magnetic flux threading the SQUID ring to control the transfer of energy, the entanglement and the statistical properties of the fields coupled to the ring. We also demonstrate that at, and around, certain values of static flux the effective coupling between the components of the system is large. The position of these regions in static flux is dependent on the energy level structure of the ring and the relative field mode frequencies, In these regions we find that the entanglement of states in the coupled system, and the energy transfer between its components, is strong.

cond-mat.supr-con↗

arXiv2004

A Fully Quantum Mechanical Model of a SQUID Ring Coupled to an Electromagnetic Field

A quantum system comprising of a monochromatic electromagnetic field coupled to a SQUID ring with sinusoidal non-linearity, is studied. A magnetostatic flux $Φ_{x}$ is also threading the SQUID ring, and is used to control the coupling between the two systems. It is shown that for special values of $Φ_{x}$ the system is strongly coupled. The time evolution of the system is studied. It is shown that exchange of energy takes place between the two modes and that the system becomes entangled. A second quasi-classical model that treats the electromagnetic field classically is also studied. A comparison between the fully quantum mechanical model with the electromagnetic field initially in a coherent state and the quasi-classical model, is made.

cond-mat.supr-con↗

arXiv2004

Photon-induced entanglement of distant mesoscopic SQUID rings

An experiment that involves two distant mesoscopic SQUID rings is studied. The superconducting rings are irradiated with correlated photons, which are produced by a single microwave source. Classically correlated (separable) and quantum mechanically correlated (entangled) microwaves are considered, and their effect on the Josephson currents is quantified. It is shown that the currents tunnelling through the Josephson junctions in the distant rings, are correlated.

quant-ph↗

arXiv2004

Entanglement of distant electron interference experiments

Two electron interference experiments which are far from each other are considered. They are irradiated with correlated nonclassical electromagnetic fields, produced by the same source. The phase factors are in this case operators, and their expectation values with respect to the density matrix of the electromagnetic field quantify the observed electron fringes. The correlated photons create correlations between the observed electron intensities. Both cases of classically correlated (separable) and quantum mechanically correlated (entangled) electromagnetic fields are considered. It is shown that the induced correlation between the distant electron interferences is sensitive to the nature of the correlation between the irradiating photons.

quant-ph↗

arXiv2003

Superconducting Analogues of Quantum Optical Phenomena: Macroscopic Quantum Superpositions and Squeezing in a SQUID Ring

In this paper we explore the quantum behaviour of a SQUID ring which has a significant Josephson coupling energy. We show that that the eigenfunctions of the Hamiltonian for the ring can be used to create macroscopic quantum superposition states of the ring. We also show that the ring potential may be utilised to squeeze coherent states. With the SQUID ring as a strong contender as a device for manipulating quantum information, such properties may be of great utility in the future. However, as with all candidate systems for quantum technologies, decoherence is a fundamental problem. In this paper we apply an open systems approach to model the effect of coupling a quantum mechanical SQUID ring to a thermal bath. We use this model to demonstrate the manner in which decoherence affects the quantum states of the ring.

quant-ph↗

arXiv2003

Correlations in interfering electrons irradiated by nonclassical microwaves

Electron interference in mesoscopic devices irradiated by external non-classical microwaves, is considered. In the case of one-mode microwaves, it is shown that both the average intensity and the spectral density of the interfering electrons are sensitive to the quantum noise of the microwaves. The results for various quantum states of the microwaves are compared and contrasted with the classical case. Separable and entangled two-mode microwaves are also considered and their effect on electron average intensity and autocorrelation, is discussed.

cond-mat↗

arXiv2002

Correlation properties of interfering electrons in a mesoscopic ring under nonclassical microwave radiation

Interfering electrons in a mesoscopic ring are irradiated with both classical and nonclassical microwaves. The average intensity of the charges is calculated as a function of time and it is found that it depends on the nature of the irradiating electromagnetic field. For various quantum states of the microwaves, the electron autocorrelation function is calculated and it shows that the quantum noise of the external field affects the interference of the charges. Two-mode entangled microwaves are also considered and the results are compared with those of the corresponding separable state. In both cases, the results depend on whether the ratio of the two frequencies is rational or irrational.

cond-mat.mes-hall↗

arXiv1996

Analytic representations based on SU(1,1) coherent states and their applications

We consider two analytic representations of the SU(1,1) Lie group: the representation in the unit disk based on the SU(1,1) Perelomov coherent states and the Barut-Girardello representation based on the eigenstates of the SU(1,1) lowering generator. We show that these representations are related through a Laplace transform. A ``weak'' resolution of the identity in terms of the Perelomov SU(1,1) coherent states is presented which is valid even when the Bargmann index $k$ is smaller than one half. Various applications of these results in the context of the two-photon realization of SU(1,1) in quantum optics are also discussed.

quant-ph↗

arXiv1996

Factorisation of analytic representations in the unit disk and number-phase statistics of a quantum harmonic oscillator

The inner-outer part factorisation of analytic representations in the unit disk is used for an effective characterisation of the number-phase statistical properties of a quantum harmonic oscillator. It is shown that the factorisation is intimately connected to the number-phase Weyl semigroup and its properties. In the Barut-Girardello analytic representation the factorisation is implemented as a convolution. Several examples are given which demonstrate the physical significance of the factorisation and its role for quantum statistics. In particular, we study the effect of phase-space interference on the factorisation properties of a superposition state.

quant-ph↗

arXiv1996

Parity-dependent squeezing of light

A parity-dependent squeezing operator is introduced which imposes different SU(1,1) rotations on the even and odd subspaces of the harmonic oscillator Hilbert space. This operator is used to define parity-dependent squeezed states which exhibit highly nonclassical properties such as strong antibunching, quadrature squeezing, strong oscillations in the photon-number distribution, etc. In contrast to the usual squeezed states whose $Q$ and Wigner functions are simply Gaussians, the parity-dependent squeezed states have much more complicated $Q$ and Wigner functions that exhibit an interesting interference in phase space. The generation of these states by parity-dependent quadratic Hamiltonians is also discussed.

quant-ph↗