arXiv subjects

Sibylle Braungardt

Publications and source records attributed to Sibylle Braungardt.

6 recordsLinked to original sources

arXiv2011

Particle Counting Statistics of Time and Space Dependent Fields

The counting statistics give insight into the properties of quantum states of light and other quantum states of matter such as ultracold atoms or electrons. The theoretical description of photon counting was derived in the 1960s and was extended to massive particles more recently. Typically, the interaction between each particle and the detector is assumed to be limited to short time intervals, and the probability of counting particles in one interval is independent of the measurements in previous intervals. There has been some effort to describe particle counting as a continuous measurement, where the detector and the field to be counted interact continuously. However, no general formula applicable to any time and space dependent field has been derived so far. In our work, we derive a fully time and space dependent description of the counting process for linear quantum many-body systems, taking into account the back-action of the detector on the field. We apply our formalism to an expanding Bose-Einstein condensate of ultracold atoms, and show that it describes the process correctly, whereas the standard approach gives unphysical results in some limits. The example illustrates that in certain situations, the back-action of the detector cannot be neglected and has to be included in the description.

quant-ph↗

arXiv2011

Atom Counting in Expanding Ultracold Clouds

We study the counting statistics of ultracold bosonic atoms that are released from an optical lattice. We show that the counting probability distribution of the atoms collected at a detector located far away from the optical lattice can be used as a method to infer the properties of the initially trapped states. We consider initial superfluid and insulating states with different occupation patterns. We analyze how the correlations between the initially trapped modes that develop during the expansion in the gravitational field are reflected in the counting distribution. We find that for detectors that are large compared to the size of the expanded wave function, the long-range correlations of the initial states can be distinguished by observing the counting statistics. We consider counting at one detector, as well as the joint probability distribution of counting particles at two detectors. We show that using detectors that are small compared to the size of the expanded wave function, insulating states with different occupation patterns, as well as supersolid states with different density distributions can be distinguished.

quant-ph↗

arXiv2010

Fermion- and spin-counting in strongly correlated systems in and out of thermal equilibrium

Atom counting theory can be used to study the role of thermal noise in quantum phase transitions and to monitor the dynamics of a quantum system. We illustrate this for a strongly correlated fermionic system, which is equivalent to an anisotropic quantum XY chain in a transverse field, and can be realized with cold fermionic atoms in an optical lattice. We analyze the counting statistics across the phase diagram in the presence of thermal fluctuations, and during its thermalization when the system is coupled to a heat bath. At zero temperature, the quantum phase transition is reflected in the cumulants of the counting distribution. We find that the signatures of the crossover remain visible at low temperature and are obscured with increasing thermal fluctuations. We find that the same quantities may be used to scan the dynamics during the thermalization of the system.

quant-ph↗

arXiv2008

Fermion- and Spin-Counting in Strongly Correlated Systems

We apply the atom counting theory to strongly correlated Fermi systems and spin models, which can be realized with ultracold atoms. The counting distributions are typically sub-Poissonian and remain smooth at quantum phase transitions, but their moments exhibit critical behavior, and characterize quantum statistical properties of the system. Moreover, more detailed characterizations are obtained with experimentally feasible spatially resolved counting distributions.

quant-ph↗

arXiv2008

Error-Resistant Distributed Quantum Computation in Trapped Ion Chain

We consider experimentally feasible chains of trapped ions with pseudo-spin 1/2, and find models that can potentially be used to implement error-resistant quantum computation. Similar in spirit to classical neural networks, the error-resistance of the system is achieved by encoding the qubits distributed over the whole system. We therefore call our system a ''quantum neural network'', and present a ''quantum neural network model of quantum computation''. Qubits are encoded in a few quasi-degenerated low energy levels of the whole system, separated by a large gap from the excited states, and large energy barriers between themselves. We investigate protocols for implementing a universal set of quantum logic gates in the system, by adiabatic passage of a few low-lying energy levels of the whole system. Naturally appearing and potentially dangerous distributed noise in the system leaves the fidelity of the computation virtually unchanged, if it is not too strong. The computation is also naturally resilient to local perturbations of the spins.

quant-ph↗

arXiv2005

Trapped ion chain as a neural network

We demonstrate the possibility of realizing a neural network in a chain of trapped ions with induced long range interactions. Such models permit to store information distributed over the whole system. The storage capacity of such network, which depends on the phonon spectrum of the system, can be controlled by changing the external trapping potential and/or by applying longitudinal local magnetic fields. The system properties suggest the possibility of implementing robust distributed realizations of quantum logic.

cond-mat.dis-nn↗