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## Quantum coherence

Coherence is one of the principal features of Quantum Mechanics. It is due to coherence that matter waves can interfere and that in the quantum world the superposition of a dead and a living cat imagined by Schroedinger can in principle exist. However, phase coherence in quantum systems can be easily lost, as a result of coupling with the environment or a measuring apparatus. This is why in everyday life we do not see superpositions of a living and a dead cat, but rather cats which are either alive or dead (and not both). However, physicists in laboratories achieve sufficient phase coherence to observe and manipulate systems in which interference plays a crucial role, and do exciting things with them. Coherent quantum systems can be used to perform tasks that have no classical counterpart like quantum cryptography, quantum teleportation, simulations of quantum dynamics of complex systems by experimentally well-controlled and easy-to-measure quantum devices, high-precision measurements beyond the shot noise limit, and, perhaps one day, a quantum computer. In order to do so, one has to work hard to keep phase coherence long enough. Among the systems behaving coherently for a relatively long time, condensed matter systems at very low temperature like superconductors and Bose-Einstein condensates, both characterized by a macroscopic number of particles involved in the formation of the ground state, have attracted recently an increasing interest.

Specific activities at the LPMMC are :

## 1) Superconducting nanocircuits

Superconducting nanocircuits based on Josephson junctions show macroscopic quantum behaviour. Level quantization, quantum tunnelling and the possibility to form superposition states have been demonstrated experimentally in such circuits, currently much studied in view of applications in quantum information processing. We analyze different types of superconducting nanocircuits theoretically, with the aim to understand their quantum properties. We include the effects that lead to decoherence such as dissipation and the presence of measuring devices.

## 2) Bose-Josephson Junctions

Josephson junctions may be realized with quantum gases by coupling two Bose-Einstein condensates, either in a double-well geometry (external Josephson effect) or by applying a Raman transition which couples two atomic states (internal Josephson effect). We have studied the quantum regime of a Bose-Josephson junction. Its dynamics following a quench of the tunnel amplitude leads to the formation of nonclassical states, e.g.Schroedinger cat states formed by superpositions of macroscopically distinct phase states. We study their nature, the possibility of imaging them and their coherence, and the effects of decoherence, which in atomic systems is mainly due to magnetic fluctuations and atom losses. The study of nonclassical atomic states has important applications to high-precision atom interferometry.

## 3) Dissipation in time-dependent quantum mechanics

The principal way to control a quantum system’s state (either to study it or to use it for something else) is to drive the system with time-dependent fields. However at the same time the system is typically coupled to an environment into which it dissipates the energy that one introduces with the drive. Here we study the subtle (and sometimes surprising) effects that occur due to the inter-play of time-dependent driving and dissipative effects (decoherence, relaxation, etc).

## 4) Dynamical models of quantum measurements

In order to describe theoretically a quantum measurement on a quantum system one has to consider the coupling of this system with a macroscopic measurement apparatus. We have considered some simple models in which this apparatus consists of a pointer with a single degree of freedom of position, which is itself coupled to an infinite bath. We have shown that the reduction of wavepacket takes place within a time which does not depend on the details of the pointer-bath coupling in the non Markovian regime, whereas in the Markov regime this time strongly depends on whether that coupling is Ohmic or super-Ohmic. The decay of the coherence of the system and pointer is in general neither exponential nor Gaussian.

## 5) Quantum correlations and their time evolution

Quantum correlations are a major ressource in quantum information processing. They can be lost due to the coupling of the system with its environment. We have studied the entanglement evolution for two qubits coupled to independent markovian baths under the monitoring of the baths by local continuous measurements (quantum trajectories). Our main result says that the average entanglement of the qubits decays exponentially. This means that the celebrated phenomenon of entanglement sudden death discovered by Diosi, Yu, and Eberly is absent if one observes the baths provoking the entanglement loss.

## Selected publications

*Physical Review Letters*

**100**, 187003 (2008)