A closed expression for the chemical potential of Bose gases in an external one-dimensional harmonic trap, reported recently in this journal (Mungan 2009 Chemical potential of one-dimensional simple harmonic oscillators Eur. J. Phys. 30 1131–6), is approximate and not applicable for temperatures lower than a characteristic value below which the ground state becomes occupied by a macroscopic number of particles. In this letter, the correct behaviour of the chemical potential at low temperature is addressed.
We report on the experimental realization and characterization of an exciton-polariton qubit prototype. In our system, a
Bose-Einstein condensate of semiconductor exciton-polaritons is confined by a spatially-patterned pump laser in an annular
trap that supports energy-degenerate circulating currents of the polariton superfluid. Using non-invasive temporal interference
measurements, we observe coherent oscillations between a pair of counter-circulating superfluid vortex states of the polaritons
coupled by elastic scattering off the laser-imprinted potential. The qubit basis states correspond to the symmetric and
antisymmetric superpositions of the two vortex states forming orthogonal double-lobe spatial wavefunctions. By engineering
the potential, we tune the coupling and coherent oscillations between the two circulating current states, control the energies of
the qubit basis states and thereby initialize the qubit in the desired state. The dynamics of the system is accurately reproduced by our theoretical two-state model, and we discuss potential avenues to achieve complete control over our polaritonic qubit and implement controllable interactions and quantum gates between such qubits.
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