Measurement of the motional sidebands of a nanogram-scale oscillator in the quantum regime

We describe measurements of the motional sidebands produced by a mechanical oscillator (with effective mass 43 ng and resonant frequency 705 kHz) that is placed in an optical cavity and cooled close to its quantum ground state. The red and blue sidebands (corresponding to Stokes and anti-Stokes scattering) from a single laser beam are recorded simultaneously via a heterodyne measurement. The oscillator’s mean phonon number ¯n is inferred from the ratio of the sidebands, and reaches a minimum value of 0.84 ± 0.22 (corresponding to a mode temperature T = 28 ± 7μK). We also infer ¯n from the calibrated area of each of the two sidebands, and from the oscillator’s total damping. The values of ¯n inferred from these four methods are in close agreement. The behavior of the sidebands as a function of the oscillator’s temperature agrees well with theory that includes the quantum fluctuations of both the cavity field and the mechanical oscillator

Two-component approach for thermodynamic properties in diluted magnetic semiconductors

We examine the feasibility of a simple description of Mn ions in III-V diluted magnetic semiconductors (DMSs) in terms of two species (components), motivated by the expectation that the Mn-hole exchange couplings are widely distributed, expecially for low Mn concentrations. We find, using distributions indicated by recent numerical mean field studies, that the thermodynamic properties (magnetization, susceptibility, and specific heat) cannot be fit by a single coupling as in a homogeneous model, but can be fit well by a two-component model with a temperature dependent number of ``strongly'' and ``weakly'' coupled spins. This suggests that a two-component description may be a minimal model for the interpretation of experimental measurements of thermodynamic quantities in III-V DMS systems.Comment: 10 pages, 9 figures, 1 new figure, substantial revision

Spin interactions and switching in vertically tunnel-coupled quantum dots

We determine the spin exchange coupling J between two electrons located in two vertically tunnel-coupled quantum dots, and its variation when magnetic (B) and electric (E) fields (both in-plane and perpendicular) are applied. We predict a strong decrease of J as the in-plane B field is increased, mainly due to orbital compression. Combined with the Zeeman splitting, this leads to a singlet-triplet crossing, which can be observed as a pronounced jump in the magnetization at in-plane fields of a few Tesla, and perpendicular fields of the order of 10 Tesla for typical self-assembled dots. We use harmonic potentials to model the confining of electrons, and calculate the exchange J using the Heitler-London and Hund-Mulliken technique, including the long-range Coulomb interaction. With our results we provide experimental criteria for the distinction of singlet and triplet states and therefore for microscopic spin measurements. In the case where dots of different sizes are coupled, we present a simple method to switch on and off the spin coupling with exponential sensitivity using an in-plane electric field. Switching the spin coupling is essential for quantum computation using electronic spins as qubits.Comment: 13 pages, 9 figure