We argue that the non-adiabatic evolution of spin states in Stern-Gerlach apparatus can blur the manifestation of path spin entanglement. This fact introduces a contradiction to the usual perception of spin measurement even in a formally ideal situation. Through quantitative calculation, we have pointed out the specific reason behind the breakdown of adiabatic evolution to be the spatial inhomogeneity of applied magnetic field. The angle $θ$ between the $z$ component of magnetic moment of the particle and applied magnetic field is also a determining factor for the category of evolution of spin states. Adiabaticity always can be restored by choosing a sufficiently small value of $θ$ . Considering azimuthal inhomogeneity, we have examined the nature of path spin entanglement in the context of Stern-Gerlach experiment.We argue that the non-adiabatic evolution of spin states in Stern-Gerlach apparatus can blur the manifestation of path spin entanglement. This fact introduces a contradiction to the usual perception of spin measurement even in a formally ideal situation. Through quantitative calculation, we have pointed out the specific reason behind the breakdown of adiabatic evolution to be the spatial inhomogeneity of applied magnetic field. The angle $θ$ between the $z$ component of magnetic moment of the particle and applied magnetic field is also a determining factor for the category of evolution of spin states. Adiabaticity always can be restored by choosing a sufficiently small value of $θ$. Considering azimuthal inhomogeneity, we have examined the nature of path spin entanglement in the context of Stern-Gerlach experiment.

arXiv:1410.4396Oct 16, 20141 citation

Magnetic resonance at the quantum limit

Patrice Bertet

Bulletin of the American Physical SocietyMar 15, 20160 citations

Semi-Classical Dynamics in Quantum Spin Systems

Jürg Martin Fröhlich, Antti Knowles, Enno Lenzmann

arXiv:0709.4561Letters in Mathematical PhysicsNov 19, 200712 citations

Numerical Engineering of Adiabatic Quantum Operations

Seyed Sahand Tabatabaei

Adiabatic quantum operations are ubiquitous in fields such as quantum information processing, quantum control, and magnetic resonance, where their high fidelity and general robustness renders them an essential tool for various applications. This inherent robustness due to adiabaticity can, however, be impaired in cases where the experimental conditions strictly require very fast evolution times. In this thesis, we provide a gradient-based numerical optimization protocol for efficiently engineering adiabatic operations, allowing for the systematic inclusion of robustness criteria against various experimental non-idealities, including inhomogeneities and uncertainties in system parameters, as well as perturbations in the Hamiltonian such as spin-spin interactions. \nThe protocol is implemented in the context of adiabatic passages for magnetic resonance, and \nit is shown that in addition to conventional adiabatic pulses, it can also generate exceptionally fast operations that although slightly deviate from adiabaticity in limited instances, still lead to a high fidelity. \nThe effectiveness of our method for addressing perturbations is also demonstrated by designing a fast adiabatic passage for dipolar-coupled electrons, and numerically comparing its performance with a pulse without such considerations.Adiabatic quantum operations are ubiquitous in fields such as quantum information processing, quantum control, and magnetic resonance, where their high fidelity and general robustness renders them an essential tool for various applications. This inherent robustness due to adiabaticity can, however, be impaired in cases where the experimental conditions strictly require very fast evolution times. In this thesis, we provide a gradient-based numerical optimization protocol for efficiently engineering adiabatic operations, allowing for the systematic inclusion of robustness criteria against various experimental non-idealities, including inhomogeneities and uncertainties in system parameters, as well as perturbations in the Hamiltonian such as spin-spin interactions. \nThe protocol is implemented in the context of adiabatic passages for magnetic resonance, and \nit is shown that in addition to conventional adiabatic pulses, it can also generate exceptionally fast operations that although slightly deviate from adiabaticity in limited instances, still lead to a high fidelity. \nThe effectiveness of our method for addressing perturbations is also demonstrated by designing a fast adiabatic passage for dipolar-coupled electrons, and numerically comparing its performance with a pulse without such considerations.

Jan 23, 20200 citations

Dissipative quantum evolution of a spin system in a magnetic field

C. Wolf

Canadian Journal of PhysicsJan 1, 19991 citation

Numerical Engineering of Robust Adiabatic Operations

Sahand Tabatabaei, Holger Haas, William Rose +7 more

Adiabatic operations are powerful tools for robust quantum control in numerous fields of physics, chemistry, and quantum information science. The inherent robustness due to adiabaticity can, however, be impaired in applications requiring short evolution times. We present a single versatile gradient-based optimization protocol that combines adiabatic control with effective Hamiltonian engineering in order to design adiabatic operations tailored to the specific imperfections and resources of an experimental setup. The practicality of the protocol is demonstrated by engineering a fast, 2.3 Rabi cycle-long adiabatic inversion pulse for magnetic resonance with built-in robustness to Rabi field inhomogeneities and resonance offsets. The performance and robustness of the pulse is validated in a nanoscale force-detected magnetic resonance experiment on a solid-state sample, indicating an ensemble-averaged inversion accuracy of 99.997%. We further showcase the utility of our protocol by providing examples of adiabatic pulses robust to spin-spin interactions, parameter-selective operations, and operations connecting arbitrary states, each motivated by experiments.Adiabatic operations are powerful tools for robust quantum control in numerous fields of physics, chemistry, and quantum information science. The inherent robustness due to adiabaticity can, however, be impaired in applications requiring short evolution times. We present a single versatile gradient-based optimization protocol that combines adiabatic control with effective Hamiltonian engineering in order to design adiabatic operations tailored to the specific imperfections and resources of an experimental setup. The practicality of the protocol is demonstrated by engineering a fast, 2.3 Rabi cycle-long adiabatic inversion pulse for magnetic resonance with built-in robustness to Rabi field inhomogeneities and resonance offsets. The performance and robustness of the pulse is validated in a nanoscale force-detected magnetic resonance experiment on a solid-state sample, indicating an ensemble-averaged inversion accuracy of 99.997%. We further showcase the utility of our protocol by providing examples of adiabatic pulses robust to spin-spin interactions, parameter-selective operations, and operations connecting arbitrary states, each motivated by experiments.

arXiv:2009.03266Physical Review AppliedApr 27, 20219 citations

θ

between the

z

component of magnetic moment of the particle and applied magnetic field is also a determining factor for the category of evolution of spin states. Adiabaticity always can be restored by choosing a sufficiently small value of

θ

. Considering azimuthal inhomogeneity, we have examined the nature of path spin entanglement in the context of Stern-Gerlach experiment.