Quantum dynamical phase transition in a system with many-body interactions | Solid State Communications

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Quantum dynamical phase transition in a system with many-body interactions

E.P. Danieli, G.A. Álvarez, P.R. Levstein, H.M. Pastawski

Facultad de Matemática, Astronomía y Física, Universidad Nacional de Córdoba, 5000 Córdoba, Argentina

Received 26 October 2006. Accepted 1 November 2006. Available online 16 November 2006. by R. Merlin.

via Quantum dynamical phase transition in a system with many-body interactions 10.1016/j.ssc.2006.11.001 : Solid State Communications | ScienceDirect.com.

Abstract

Recent experiments, [G.A. Álvarez, E.P. Danieli, P.R. Levstein, H.M. Pastawski, J. Chem. Phys. 124 (2006) 194507], have reported the observation of a quantum dynamical phase transition in the dynamics of a spin swapping gate. In order to explain this result from a microscopic perspective, we introduce a Hamiltonian model of a two level system with many-body interactions with an environment whose excitation dynamics is fully solved within the Keldysh formalism. If a particle starts in one of the states of the isolated system, the return probability oscillates with the Rabi frequency ω0. For weak interactions with the environment View the MathML source, we find a slower oscillation whose amplitude decays with a rate View the MathML source. However, beyond a finite critical interaction with the environment, View the MathML source, the decay rate becomes View the MathML source. The oscillation period diverges showing a quantum dynamical phase transition to a Quantum Zeno phase consistent with the experimental observations.

Environmentally induced quantum dynamical phase transition in the spin swapping operation | Journal of Chemical Physics

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Environmentally induced quantum dynamical phase transition in the spin swapping operation

Gonzalo A. Álvarez, Ernesto P. Danieli, Patricia R. Levstein, and Horacio M. Pastawski

Facultad de Matemática, Astronomía y Física, Universidad Nacional de Córdoba, Ciudad Universitaria, 5000, Córdoba, Argentina

via Environmentally induced quantum dynamical phase transition in the spin swapping operation | Browse – Journal of Chemical Physics.

Quantum information processing relies on coherent quantum dynamics for a precise control of its basic operations. A swapping gate in a two-spin system exchanges the degenerate states ∣↑, ↓⟩ and ∣↓, ↑⟩. In NMR, this is achieved turning on and off the spin-spin interaction b = ΔE that splits the energy levels and induces an oscillation with a natural frequency ΔE/. Interaction of strength /τSE, with an environment of neighboring spins, degrades this oscillation within a decoherence time scale τϕ. While the experimental frequency ω and decoherence time τϕ were expected to be roughly proportional to b/ and τSE, respectively, we present here experiments that show drastic deviations in both ω and τϕ. By solving the many spin dynamics, we prove that the swapping regime is restricted to ΔEτSE. Beyond a critical interaction with the environment the swapping freezes and the decoherence rate drops as 1/τϕ∝(b/)2τSE. The transition between quantum dynamical phases occurs when ωmath becomes imaginary, resembling an overdamped classical oscillator. Here, 0 ⩽ k2 ⩽ 1 depends only on the anisotropy of the system-environment interaction, being 0 for isotropic and 1 for XY interactions. This critical onset of a phase dominated by the quantum Zeno effect opens up new opportunities for controlling quantum dynamics.

© 2006 American Institute of Physics

Decoherence rate and oscillation frequency in the spin swapping of a 13C-1H system. Data points are obtained from cross polarization experiments. The zero plateau in the frequency and the parabolic behavior of the decoherence rate are indicative of an over-damped Zeno phase. Solid lines are the prediction of our model.
Decoherence rate and oscillation frequency in the spin swapping of a 13C-1H system. Data points are obtained from cross polarization experiments. The zero plateau in the frequency and the parabolic behavior of the decoherence rate are indicative of an over-damped Zeno phase. Solid lines are the prediction of our model.
Quantum dynamical phase diagram for the spin swapping operation. The figure shows the frequency dependence on system-environment (SE) interaction anisotropy pXY and the ratio among the internal and the SE interaction. The projection plane determines the phase diagram where the transition between the swapping phase into the Zeno phase (frequency null) is manifested. Values of pXY for typical SE interaction
Quantum dynamical phase diagram for the spin swapping operation. The figure shows the frequency dependence on system-environment (SE) interaction anisotropy pXY and the ratio among the internal and the SE interaction. The projection plane determines the phase diagram where the transition between the swapping phase into the Zeno phase (frequency null) is manifested. Values of pXY for typical SE interaction

Quantum dynamics under coherent and incoherent effects of a spin bath in the Keldysh formalism: application to a spin swapping operation | Chemical Physics Letters

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Quantum dynamics under coherent and incoherent effects of a spin bath in the Keldysh formalism: application to a spin swapping operation

Ernesto P. Danieli,

Horacio M. PastawskiCorresponding author contact information, E-mail the corresponding author,

Gonzalo A. Álvarez

Facultad de Matemática, Astronomía y Física, Universidad Nacional de Córdoba, Ciudad Universitaria, 5000 Córdoba, Argentina

Received 30 March 2004. Revised 20 October 2004. Available online 22 December 2004.

via Quantum dynamics under coherent and incoherent effects of a spin bath in the Keldysh formalism: application to a spin swapping operation 10.1016/j.cplett.2004.11.056 : Chemical Physics Letters | ScienceDirect.com.

Abstract

We develop the Keldysh formalism for the polarization dynamics of an open spin system. We apply it to the swapping between two qubit states in a model describing an NMR cross-polarization experiment. The environment is a set of interacting spins. For fast fluctuations in the environment, the analytical solution shows effects missed by the secular approximation of the quantum master equation for the density matrix: a frequency decrease depending on the system-environment escape rate and the quantum quadratic short time behavior. Considering full memory of the bath correlations yields a progressive change of the swapping frequency.

Many-spin quantum dynamics during cross polarization in 8CB | Journal of Chemical Physics

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Many-spin quantum dynamics during cross polarization in 8CB

Ana K. Chattah1, Gonzalo A. Álvarez1, Patricia R. Levstein1, Fernando M. Cucchietti1, Horacio M. Pastawski1, Jésus Raya2, and Jérôme Hirschinger2

via Many-spin quantum dynamics during cross polarization in 8CB | Browse – Journal of Chemical Physics.

1Facultad de Matemática, Astronomía y Física, Universidad Nacional de Córdoba, Ciudad Universitaria, 5000 Córdoba, Argentina

2Laboratoire de RMN de la Matière Condensée, Institut Le bel, Université Louis Pasteur, 67000, Strasbourg, France

(Received 12 May 2003; accepted 23 July 2003)

We analyze theoretically and experimentally the quantum dynamics of a three-spin-1/2 system during cross polarization (CP). Our analysis takes into account a Hamiltonian behavior for a carbon 13C coupled to two protons 1H while the coupling to a spin bath is treated in the fast fluctuation approximation. This model is applied to the methylene and biphenyl groups of the smectic and nematic phases of the liquid crystal 4-n-octyl-4′-cyanobiphenyl (8CB). Experimental data from standard CP, combined with our theoretical results, allow us to separate the homonuclear 1H–1H and heteronuclear 1H–13C residual dipolar couplings. These values are in good agreement with those obtained by using a combination of CP under Lee–Goldburg conditions and standard CP data. A well differentiated relaxation behavior among the two phases seems to indicate that while the extreme narrowing approximation is appropriate for the nematic phase, the description of the smectic phase requires consideration of the slow-motion limit. © 2003 American Institute of Physics.

© 2003 American Institute of Physics

13C polarization as a function of contact time tc for aromatic and aliphatic carbons in a standard CP experiment at 300 K smectic phase. Fittings of the experimental data to the anisotropic, isotropic, and purely dipolar models described in the text.
13C polarization as a function of contact time tc for aromatic and aliphatic carbons in a standard CP experiment at 300 K smectic phase. Fittings of the experimental data to the anisotropic, isotropic, and purely dipolar models described in the text.