We discuss methods for coherently controlling mesoscopic atomic ensembles where the number of atoms varies randomly from one experimental run to the next. The proposed schemes are based on adiabatic passage and Rydberg blockade and can be used for implementation of a scalable quantum register formed by an array of randomly loaded optical dipole traps.

We present schemes for geometric phase compensation in an adiabatic passage which can be used for the implementation of quantum logic gates with atomic ensembles consisting of an arbitrary number of strongly interacting atoms. Protocols using double sequences of stimulated Raman adiabatic passage (STIRAP) or adiabatic rapid passage (ARP) pulses are analyzed. Switching the sign of the detuning between two STIRAP sequences, or inverting the phase between two ARP pulses, provides state transfer with well-defined amplitude and phase independent of atom number in the Rydberg blockade regime. Using these pulse sequences we present protocols for universal single-qubit and two-qubit operations in atomic ensembles containing an unknown number of atoms.

We propose the use of Rydberg interactions and ensembles of cold atoms in mixed state for the implementation of a protocol for deterministic quantum computation with one quantum bit that can be readily operated in high dimensional Hilbert spaces. We propose an experimental test for the scalability of the protocol and to study the physics of discord. Furthermore, we explore the possibility of extending to non-trivial unitaries, such as those associated to many-body physics. Finally develop a scheme to add control to cold atom unitaries in order to facilitate their implementation in our proposal.At present, no single feature of the quantum world has been identified as the source of the computational enhancement, efficiency and speed-up of quantum protocols. Whilst entanglement is widely recognized as a key resource in quantum technology [1], an advantage over classical computing could be achieved without it [2] in the presence of non-classical correlations (discord). Experiments using few photonic qubits [3] have shown that some computational tasks can be efficiently solved even with no entanglement. As entanglement is

We analyze the operation of a sensor based on atom interferometry, which can achieve supraclassical sensitivity by exploiting quantum correlations in mixed states of many qubits. The interferometer is based on quantum gates which use coherently controlled Rydberg interactions between a single atom (which acts as a control qubit) and an atomic ensemble (which provides register qubits). In principle, our scheme can achieve precision scaling with the size of the ensemble-which can extend to large numbers of atoms-while using only single-qubit operations on the control and bulk operations on the ensemble. We investigate realistic implementation of the interferometer, and our main aim is to develop an approach to quantum metrology that can achieve quantum-enhanced measurement precision by exploiting coherent operations on large impure quantum states. We propose an experiment to demonstrate the enhanced sensitivity of the protocol and to investigate a transition from classical to supraclassical sensitivity which occurs when using highly mixed probe states.

The structure of the Cooper minima in the transition probabilities and photoionization crosssections for low-excited and Rydberg nS, nP, nD and nF states of alkali-metal atoms has been studied using a Coulomb approximation and a quasiclassical model. The range of applicability of the quasiclassical model has been defined from comparison with available experimental and theoretical data on dipole moments, oscillator strengths, and photoionization cross-sections. A new Cooper minimum for transitions between rubidium Rydberg states has been found.