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Register a new userExperimental demonstration of the stability of Berrys phase for a spin-1/2 particle
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The geometric phase has been proposed as a candidate for noise resilient coherent manipulation of fragile quantum systems. Since it is determined only by the path of the quantum state, the presence of noise fluctuations affects the geometric phase in a different way than the dynamical phase. We have experimentally tested the robustness of Berrys geometric phase for spin-1/2 particles in a cyclically varying magnetic field. Using trapped polarized ultra-cold neutrons it is demonstrated that the geometric phase contributions to dephasing due to adiabatic field fluctuations vanish for long evolution times.
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In this paper we define a non-dynamical phase for a spin-1/2 particle in a rotating magnetic field in the non-adiabatic non-cyclic case, and this phase can be considered as a generalized Berry phase. We show that this phase reduces to the geometric Berry phase, in the adiabatic limit, up to a factor independent of the parameters of the system. We could add an arbitrary phase to the eigenstates of the Hamiltonian due to the gauge freedom. Then, we fix this arbitrary phase by comparing our Berry phase in the adiabatic limit with the Berrys result for the same system. Also, in the extreme non-adiabatic limit our Berry phase vanishes, modulo $2pi$, as expected. Although, our Berry phase is in general complex, it becomes real in the expected cases: the adiabatic limit, the extreme non-adiabatic limit, and the points at which the state of the system returns to its initial form, up to a phase factor. Therefore, this phase can be considered as a generalization of the Berry phase. Moreover, we investigate the relation between the value of the generalized Berry phase, the period of the states and the period of the Hamiltonian.
Geometrical phases have been applied in virtually every major branch of physics and they play an important role in topology and knot theory in mathematics and quantum computation. However, most of the early works focus on pure quantum states which are very unrealistic and almost never occur in practice. The two existed definitions -Uhlmanns and Sj{o}qvists- would result in different values for the geometric phase in general. The definition of geometric phase in mixed state scenario is still an open question. Here we present a unified framework for both approaches within one and the same formalism based on simple interferometry. We then present experimental results which confirm both approaches to mixed state geometric phase and clearly demonstrate that their unification is possible. Our experiments are furthermore the first such to measure Uhlmanns mixed state geometric phase and show in addition that it is different to the Sj{o}qvists phase.
The 1:1:2 resonant elastic pendulum is a simple classical system that displays the phenomenon known as Hamiltonian monodromy. With suitable initial conditions, the system oscillates between nearly pure springing and nearly pure elliptical-swinging motions, with sequential major axes displaying a stepwise precession. The physical consequence of monodromy is that this stepwise precession is given by a smooth but multivalued function of the constants of motion. We experimentally explore this multivalued behavior. To our knowledge, this is the first experimental demonstration of classical monodromy.
Although the quantum classical Liouville equation (QCLE) arises by cutting off the exact equation of motion for a coupled nuclear-electronic system at order 1 (1 = $hbar^0$ ), we show that the QCLE does include Berrys phase effects and Berrys forces (which are proportional to a higher order, $hbar$ = $hbar^1$ ). Thus, the fundamental equation underlying mixed quantum-classical dynamics does not need a correction for Berrys phase effects and is valid for the case of complex Hamiltonians. Furthermore, we also show that, even though Tullys surface hopping model ignores Berrys phase, Berrys phase effects are included automatically within Ehrenfest dynamics. These findings should be of great importance if we seek to model coupled nuclear-electronic dynamics for systems with spin-orbit coupling, where the complex nature of the Hamiltonian is paramount.
We report the experimental demonstration of continuous variable cloning of phase conjugate coherent states as proposed by Cerf and Iblisdir (Phys. Rev. Lett. 87, 247903 (2001)). In contrast to the proposal of Cerf and Iblisdir, the cloning transformation is accomplished using only linear optical components, homodyne detection and feedforward. Three clones are succesfully produced with fidelities about 89%.
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