Spin-Orbit Coupling and Time-Reversal Symmetry in Quantum Gates

We study the effect of spin-orbit coupling on quantum gates produced by pulsing the exchange interaction between two single electron quantum dots. Spin-orbit coupling enters as a small spin precession when electrons tunnel between dots. For adiabatic pulses the resulting gate is described by a unitary operator acting on the four-dimensional Hilbert space of two qubits. If the precession axis is fixed, time-symmetric pulsing constrains the set of possible gates to those which, when combined with single qubit rotations, can be used in a simple CNOT construction. Deviations from time-symmetric pulsing spoil this construction. The effect of time asymmetry is studied by numerically integrating the Schr\"odinger equation using parameters appropriate for GaAs quantum dots. Deviations of the implemented gate from the desired form are shown to be proportional to dimensionless measures of both spin-orbit coupling and time asymmetry of the pulse.Comment: 10 pages, 3 figure

Quantum Computation and Spin Electronics

In this chapter we explore the connection between mesoscopic physics and quantum computing. After giving a bibliography providing a general introduction to the subject of quantum information processing, we review the various approaches that are being considered for the experimental implementation of quantum computing and quantum communication in atomic physics, quantum optics, nuclear magnetic resonance, superconductivity, and, especially, normal-electron solid state physics. We discuss five criteria for the realization of a quantum computer and consider the implications that these criteria have for quantum computation using the spin states of single-electron quantum dots. Finally, we consider the transport of quantum information via the motion of individual electrons in mesoscopic structures; specific transport and noise measurements in coupled quantum dot geometries for detecting and characterizing electron-state entanglement are analyzed.Comment: 28 pages RevTeX, 4 figures. To be published in "Quantum Mesoscopic Phenomena and Mesoscopic Devices in Microelectronics," eds. I. O. Kulik and R. Ellialtioglu (NATO Advanced Study Institute, Turkey, June 13-25, 1999

Full control of qubit rotations in a voltage-biased superconducting flux qubit

We study a voltage-controlled version of the superconducting flux qubit [Chiorescu et al., Science 299, 1869 (2003)] and show that full control of qubit rotations on the entire Bloch sphere can be achieved. Circuit graph theory is used to study a setup where voltage sources are attached to the two superconducting islands formed between the three Josephson junctions in the flux qubit. Applying a voltage allows qubit rotations about the y axis, in addition to pure x and z rotations obtained in the absence of applied voltages. The orientation and magnitude of the rotation axis on the Bloch sphere can be tuned by the gate voltages, the external magnetic flux, and the ratio alpha between the Josephson energies via a flux-tunable junction. We compare the single-qubit control in the known regime alpha<1 with the unexplored range alpha>1 and estimate the decoherence due to voltage fluctuations.Comment: 12 pages, 12 figures, 1 tabl

Nuclear State Preparation via Landau-Zener-Stueckelberg transitions in Double Quantum Dots

We theoretically model a nuclear-state preparation scheme that increases the coherence time of a two-spin qubit in a double quantum dot. The two-electron system is tuned repeatedly across a singlet-triplet level-anticrossing with alternating slow and rapid sweeps of an external bias voltage. Using a Landau-Zener-Stueckelberg model, we find that in addition to a small nuclear polarization that weakly affects the electron spin coherence, the slow sweeps are only partially adiabatic and lead to a weak nuclear spin measurement and a nuclear-state narrowing which prolongs the electron spin coherence. This resolves some open problems brought up by a recent experiment [D. J. Reilly et al., Science 321, 817 (2008).]. Based on our description of the weak measurement, we simulate a system with up to n=200 nuclear spins per dot. Scaling in n indicates a stronger effect for larger n.Comment: 4.1 pages, 2 figure

Double-Occupancy Errors, Adiabaticity, and Entanglement of Spin-Qubits in Quantum Dots

Quantum gates that temporarily increase singlet-triplet splitting in order to swap electronic spins in coupled quantum dots, lead inevitably to a finite double-occupancy probability for both dots. By solving the time-dependent Schr\"odinger equation for a coupled dot model, we demonstrate that this does not necessarily lead to quantum computation errors. Instead, the coupled dot ground state evolves quasi-adiabatically for typical system parameters so that the double-occupancy probability at the completion of swapping is negligibly small. We introduce a measure of entanglement which explicitly takes into account the possibilty of double occupancies and provides a necessary and sufficient criterion for entangled states.Comment: 9 pages, 4 figures include

Entangled photons from the polariton vacuum in a switchable optical cavity

We study theoretically the entanglement of two-photon states in the ground state of the intersubband cavity system, the so-called polariton vacuum. The system consists of a sequence of doped quantum wells located inside a microcavity and the photons can interact with intersubband excitations inside the quantum wells. Using an explicit solution for the ground state of the system, operated in the ultrastrong coupling regime, a post-selection is introduced, where only certain two-photon states are considered and analyzed for mode entanglement. We find that a fast quench of the coupling creates entangled photons and that the degree of entanglement depends on the absolute values of the in-plane wave vectors of the photons. Maximally entangled states can be generated by choosing the appropriate modes in the post-selection.Comment: 9+ pages, 7 figure

Entanglement detection for electrons via witness operators

We discuss an implementation of the entanglement witness, a method to detect entanglement with few local measurements, in systems where entangled electrons are generated both in the spin and orbital degrees of freedom. We address the efficiency of this method in various setups, including two different particle-hole entanglement structures, and we demonstrate that it can also be used to infer information on the possible dephasing afflicting the devices.Comment: 12 pages, 5 figures; published versio

Spectra of ultrabroadband squeezed pulses and the finite-time Unruh-Davies effect

We study spectral properties of quantum radiation of ultimately short duration. In particular, we introduce a continuous multimode squeezing operator for the description of subcycle pulses of entangled photons generated by a coherent-field driving in a thin nonlinear crystal with second order susceptibility. We find the ultrabroadband spectra of the emitted quantum radiation perturbatively in the strength of the driving field. These spectra can be related to the spectra expected in an Unruh-Davies experiment with a finite time of acceleration. In the time domain, we describe the corresponding behavior of the normally ordered electric field variance.Comment: 11 pages, 5 figure