Optically induced rotation of an exciton spin in a semiconductor quantum dot.

We demonstrate control over the spin state of a semiconductor quantum dot exciton using a polarized picosecond laser pulse slightly detuned from a biexciton resonance. The control pulse follows an earlier pulse, which generates an exciton and initializes its spin state as a coherent superposition of its two nondegenerate eigenstates. The control pulse preferentially couples one component of the exciton state to the biexciton state, thereby rotating the exciton's spin direction. We detect the rotation by measuring the polarization of the exciton spectral line as a function of the time difference between the two pulses. We show experimentally and theoretically how the angle of rotation depends on the detuning of the second pulse from the biexciton resonance.

Entanglement on demand through time reordering.

Entangled photons can be generated "on demand" in a novel scheme involving unitary time reordering of the photons emitted in a radiative decay cascade. The scheme yields polarization entangled photon pairs, even though prior to reordering the emitted photons carry significant "which path information" and their polarizations are unentangled. This shows that quantum chronology can be manipulated in a way that is lossless and deterministic (unitary). The theory can, in principle, be tested and applied to the biexciton cascade in semiconductor quantum dots.

Entangled photon pairs from semiconductor quantum dots.

Tomographic analysis demonstrates that the polarization state of pairs of photons emitted from a biexciton decay cascade becomes entangled when spectral filtering is applied. The measured density matrix of the photon pair satisfies the Peres criterion for entanglement by more than 3 standard deviations of the experimental uncertainty and violates Bell's inequality. We show that the spectral filtering erases the "which path" information contained in the photons' color and that the remanent information in the quantum dot degrees of freedom is negligible.

Adiabatic swimming in an ideal quantum gas.

Interference effects are important for swimming of mesoscopic systems that are small relative to the coherence length of the surrounding quantum medium. Swimming is geometric for slow swimmers and the distance covered in each stroke is determined, explicitly, in terms of the on-shell scattering matrix. Remarkably, for a one-dimensional Fermi gas at zero temperature we find that slow swimming is topological: the swimming distance covered in one stroke is quantized in half integer multiples of the Fermi wavelength. In addition, a careful choice of the swimming stroke can eliminate dissipation.

Optimal swimming at low Reynolds numbers.

Efficient swimming at low Reynolds numbers is a major concern of microbots. To compare the efficiencies of different swimmers we introduce the notion of "a swimming drag coefficient" which allows for the ranking of swimmers. We find the optimal swimmer within a certain class of two-dimensional swimmers using conformal mapping techniques.

Optimal rotations of deformable bodies and orbits in magnetic fields.

Deformations can induce rotation with zero angular momentum where dissipation is a natural "cost function." This gives rise to an optimization problem of finding the most effective rotation with zero angular momentum. For certain plastic and viscous media in two dimensions the optimal path is the orbit of a charged particle on a surface of constant negative curvature with a magnetic field whose total flux is half a quantum unit.

Semiclassical analysis and the magnetization of the Hofstadter model.

The magnetization and the de Haas-van Alphen oscillations of Bloch electrons are calculated near commensurate magnetic fluxes. Two phases that appear in the quantization of mixed systems--the Berry phase and a phase first discovered by Wilkinson--play a key role in the theory.

Optimal quantum pumps.

We study adiabatic quantum pumps on time scales that are short relative to the cycle of the pump. In this regime the pump is characterized by the matrix of energy shift which we introduce as the dual to Wigner's time delay. The energy shift determines the charge transport, the dissipation, the noise, and the entropy production. We prove a general lower bound on dissipation in a quantum channel and define optimal pumps as those that saturate the bound. We give a geometric characterization of optimal pumps and show that they are noiseless and transport integral charge in a cycle. Finally we discuss an example of an optimal pump related to the Hall effect.