arXiv subjects

P. Marecki

Publications and source records attributed to P. Marecki.

10 recordsLinked to original sources

arXiv2012

On the wave equation in spacetimes of Goedel type

We analyze the d'Alembert equation in the Goedel-type spacetimes with spherical and Lobachevsky sections (with sufficiently rapid rotation). By separating the $t$ and $x_3$ dependence we reduce the problem to a group-theoretical one. In the spherical case solutions have discrete frequencies, and involve spin-weighted spherical harmonics. In the Lobachevsky case we give simple formulas for obtaining all the solutions belonging to the $D^\pm_\la$ sectors of the irreducible unitary representations of the reduced Lorentz group. The wave equation enforces restrictions on $\la$ and the allowed (here: continuous) spectrum of frequencies.

gr-qc↗

arXiv2008

A vortex model for rotating compact objects

A rotating stationary solution of the vacuum Einstein equations with a cosmological constant is exhibited which reduces to de Sitter's interior cosmological solution when the angular momentum goes to zero. This solution is locally isomorphic to de Sitter space, but as one approaches the axis of rotation a conical event horizon appears that signals the appearance of a new phase of space-time. This suggests that in reality rotating compact objects have a vortex structure similar to that conjectured for rotating superfluid droplets. In the limit of slow rotation the vortex core would be nearly cylindrical and the space-time inside the core would be Godel-like. The exterior space-time will resemble the Kerr solution for equatorial latitudes, but significant deviations from Kerr are expected for polar latitudes.

astro-ph↗

arXiv2008

Balanced homodyne detectors and Casimir energy densities

We recall and generalize the analysis of the output of the so-called balanced homodyne detectors. The most important feature of these detectors is their ability to quantify the vacuum fluctuations of the electric field, that is expectation values of products of (quantum-) electric-field operators. More precisely, the output of BHDs provides information on the one- and two-point functions of arbitrary states of quantum fields. We generalize the analysis of the response of BHDs to the case of quantum fields under influence of static external conditions such as cavities or polarizable media. By recalling the expressions for two-point functions of quantum fields in Casimir geometries we show, that a rich, position- and frequency-dependent pattern of BHD responses is predicted for ground states. This points to a potentially new characterization of quantum fields in Casimir setups which would not only complement the current global methods (Casimir forces), but also improve understanding of sub-vacuum energy densities present in some regions in these geometries.

quant-ph↗

arXiv2008

Balanced homodyne detectors in QFT

Within the dipole approximation we describe the interaction of a photodiode with the quantum electric field. The diode is modelled by an electron in a bound state which upon interaction, treated perturbatively in the paper, can get excited to one of the scattering states. We furthermore analyze a balanced homodyne detector (BHD) with a local oscillator (LO) consisting of two photodiodes illuminated by a monochromatic coherent state. We show, that to the leading order the BHD's output measures the expectation value of the quantum electric field, in the state without the LO, restricted to the frequency of the LO. The square of the output measures the two-point function of the quantum field. This shows that the BHDs provide tools for measurements of sub-vacuum (negative) expectation values of the squares quantum fields and thus for test of Quantum Energy Inequality - like bounds, or other QFT effects under the influence of external conditions.

quant-ph↗

arXiv2007

Rotating De Sitter Space

An exact solution of the vacuum Einstein equations with a cosmological constant is exhibited which can perhaps be used to describe the interior of compact rotating objects. The physical part of this solution has the topology of a torus, which may shed light on the origin of highly collimated jets from compact objects.

gr-qc↗

arXiv2006

On quantum effects in the vicinity of would-be horizons

We present a method based on the so-called Quantum Energy Inequalities, which allows to compare, and bound, the expectation values of energy-densities of ground states of quantum fields in spacetimes possessing isometric regions. The method supports the conclusion, that the Boulware energy density is universal both: at modest (and far) distances from compact spherical objects, and close to the would-be horizons of the gravastar/QBHO spacetimes. It also provides a natural consistency check for concrete (approximate, numerical) calculations of the expectation values of the energy-momentum tensors.

gr-qc↗

arXiv2005

Bounds on the energy densities of ground states on static spacetimes of compact objects

In this paper we investigate quantum fields propagating on given, static, spherically symmetric spacetimes, which are isometric to a part of the Schwarzschild spacetime. Without specifying the internal geometry we show, that there exist bounds on the energy densities of ground states of a quantum scalar field on such spacetimes. The bounds (from above and below) come from the so-called Quantum Energy Inequalities, and are centered around the energy density of the Boulware state (the ground state for Schwarzschild spacetime). The specific value of the bound from below depends critically on the distance $\ell$ from the horizon, where the spacetimes of compact objects cease to be isometric to the Schwarzschild spacetime. In the limit of small $\ell$ we prove, that the energy densities of ground states cannot be below the Boulware level.

gr-qc↗

arXiv2005

Spontaneous emission of light from atoms: the model

We investigate (non-relativistic) atomic systems interacting with quantum electromagnetic field (QEF). The resulting model describes spontaneous emission of light from a two-level atom surrounded by various initial states of the QEF. We assume, that the quantum field interacts with the atom via the standard, minimal-coupling Hamiltonian, with the $A^2$ term neglected. We also assume, that there will appear at most single excitations (photons). By conducting the analysis on a general level we allow for an arbitrary initial state of the QEF (which can be for instance: the vacuum, the ground state in a cavity, or the squeezed state). We derive a Volterra-type equation which governs the time evolution of the amplitude of the excited state. The two-point function of the initial state of the QEF, integrated with a combination of atomic wavefunctions, forms the kernel of this equation.

quant-ph↗

arXiv2004

Application of quantum inequalities to quantum optics

We establish a connection between quantum inequalities (known from quantum field theory on curved spacetimes) and the degree of squeezing in quantum-optical experiments. We prove an inequality which binds the reduction of the electric-field fluctuations to their duration. The bigger the level of fluctuations-suppression the shorter its duration. As an example of the application of this inequality in the case of squeezed light whose phase is controlled with 1% accuracy we derive a limit of -15dB on the allowed degree of squeezing.

quant-ph↗

arXiv2004

Quantum Electrodynamics on background external fields

The quantum electrodynamics in presence of background external fields is developed. Modern methods of local quantum physics allow to formulate the theory on arbitrarily strong possibly time-dependent external fields. Non-linear observables which depend only locally on the external field are constructed. The tools necessary for this formulation, the parametrices of the Dirac operator, are investigated.

hep-th↗