# HAWKINGINTHELAB Résumé de rapport

Project ID:
500783

Financé au titre de:
FP6-MOBILITY

Pays:
Hungary

## Final Activity Report Summary - HAWKINGINTHELAB (Hawking radiation in the laboratory: quantum field theory in singular media)

We studied a variety of quantum optical systems with theoretical methods. One of our goals was to analyse the possibility of the emergence of an analogy to radiation in curved space-time, first predicted by Hawking. A defining property of such radiation is the maximal entanglement between separate modes. This property turned out to be of fundamental importance from the point of view of handling quantum information. A related question we addressed was how quantum field theoretical effects in general can be utilized in quantum optical systems, especially for the generation and manipulation of entanglement and its potential applications. Part of the present research aimed at better understanding the nature of entanglement, its theoretical description and quantification in arbitrary quantum optical systems.

Wave catastrophes are characterised by logarithmic phase singularities in a field theory. Examples are light at the horizon of a black hole, sound in trans-sonic fluids, waves in accelerated frames, light in singular dielectrics and slow light close to a zero of the group velocity. We showed that there exists a universal property of solutions of the singular wave equation: the wave amplitude grows with a half-integer power for mono-directional and symmetric wave catastrophes.

Moving Bose-Einstein condensates of alkali atoms with speed exceeding the local velocity of sound are promising candidates to establish the laboratory analog of the event horizon and to measure the acoustic version of Hawking radiation. We determined the conditions for supersonic flow and the Hawking temperature for realistic condensates on waveguides where an external potential plays the role of a supersonic nozzle. In our quasi one-dimensional model the transition to supersonic speed occurs at the maximum value of the external potential. In this model we found that the Hawking temperature is entirely determined by the curvature of the potential.

A collective system of atoms in a high-quality cavity can be described by a nonlinear interaction, which arises due to field theoretical reasons, i.e. the Lamb shift of the energy levels by the cavity. We showed how this collective interaction can be used to create entanglement and perform quantum logic. In particular, we produced schemes to realize controlled-not gates not only for two-qubit but also for three-qubit systems.

The transfer of quantum information involves three types of resources: direct transfer of quantum systems, previously shared entanglement, and classical communication. These resources are not independent of each other. We showed that the simulation of measurement statistics in a particular quantum communication protocol is not possible for arbitrary states. In addition, we determined all the ensembles that can be remotely prepared in a deterministic and oblivious way using a non-maximally entangled resource with minimum classical communication cost when Bob's unitary transformations form a cyclic group.

In order to relate entanglement and non-classicality of a quantum state, we proposed the entanglement potential (EP) as a measure of non-classicality for quantum state. It is the amount of two-mode entanglement that can be generated from the field using linear optics, auxiliary classical states, and ideal photodetectors.

Wave catastrophes are characterised by logarithmic phase singularities in a field theory. Examples are light at the horizon of a black hole, sound in trans-sonic fluids, waves in accelerated frames, light in singular dielectrics and slow light close to a zero of the group velocity. We showed that there exists a universal property of solutions of the singular wave equation: the wave amplitude grows with a half-integer power for mono-directional and symmetric wave catastrophes.

Moving Bose-Einstein condensates of alkali atoms with speed exceeding the local velocity of sound are promising candidates to establish the laboratory analog of the event horizon and to measure the acoustic version of Hawking radiation. We determined the conditions for supersonic flow and the Hawking temperature for realistic condensates on waveguides where an external potential plays the role of a supersonic nozzle. In our quasi one-dimensional model the transition to supersonic speed occurs at the maximum value of the external potential. In this model we found that the Hawking temperature is entirely determined by the curvature of the potential.

A collective system of atoms in a high-quality cavity can be described by a nonlinear interaction, which arises due to field theoretical reasons, i.e. the Lamb shift of the energy levels by the cavity. We showed how this collective interaction can be used to create entanglement and perform quantum logic. In particular, we produced schemes to realize controlled-not gates not only for two-qubit but also for three-qubit systems.

The transfer of quantum information involves three types of resources: direct transfer of quantum systems, previously shared entanglement, and classical communication. These resources are not independent of each other. We showed that the simulation of measurement statistics in a particular quantum communication protocol is not possible for arbitrary states. In addition, we determined all the ensembles that can be remotely prepared in a deterministic and oblivious way using a non-maximally entangled resource with minimum classical communication cost when Bob's unitary transformations form a cyclic group.

In order to relate entanglement and non-classicality of a quantum state, we proposed the entanglement potential (EP) as a measure of non-classicality for quantum state. It is the amount of two-mode entanglement that can be generated from the field using linear optics, auxiliary classical states, and ideal photodetectors.