Levitated optomechanical systems, and particularly particles trapped in vacuum, provide unique platforms for studying the mechanical behavior of objects well-isolated from their environment. Ultimately, such systems may enable the study of fundamental questions in quantum mechanics, gravity, and other weak forces. While the optical trapping of nanoparticles has emerged as the prototypical levitated optomechanical system, it is not without problems due to the heating from the high optical intensity required, particularly when combined with a high vacuum environment. Here we investigate a magneto-gravitational trap in ultra-high vacuum. In contrast to optical trapping, we create an entirely passive trap for diamagnetic particles by utilizing the magnetic field generated by permanent magnets and the gravitational interaction. We demonstrate cooling the center of mass motion of a trapped silica microsphere from ambient temperature to an effective temperature near or below one milliKelvin in two degrees of freedom by optical feedback damping.

While it is often thought that the geometric phase is less sensitive to fluctuations in the control fields, a very general feature of adiabatic Hamiltonians is the unavoidable dynamic phase that accompanies the geometric phase. The effect of control field noise during adiabatic geometric quantum gate operations has not been probed experimentally, especially in the canonical spin qubit system that is of interest for quantum information. We present measurement of the Berry phase and carry out adiabatic geometric phase gate in a single solid-state spin qubit associated with the nitrogen-vacancy center in diamond. We manipulate the spin qubit geometrically by careful application of microwave radiation that creates an effective rotating magnetic field, and observe the resulting Berry phase signal via spin echo interferometry. Our results show that control field noise at frequencies higher than the spin echo clock frequency causes decay of the quantum phase, and degrades the fidelity of the geometric phase gate to the classical threshold after a few (∼10) operations. This occurs inspite of the geometric nature of the state preparation, due to unavoidable dynamic contributions. We have carried out systematic analysis and numerical simulations to study the effects of the control field noise and imperfect driving waveforms on the quantum phase gate.

Optomechanical systems composed of levitated particles in vacuum provide excellent conditions to test the predictions of both classical and quantum physics. While similar in approach, differing experimental setups used to achieve levitation and trapping provide unique parameter regimes for study. In this work, we show that the highly anisotropic and deep potential well provided by a magnetogravitational trap allows the creation of a micrometer-scale “molecule” consisting of two like-charged microspheres in a harmonic potential. We demonstrate the detection and manipulation (excitation and cooling) of two distinct modes of the microsphere molecule motion along the weakest trap axis.

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