Ornstein-Uhlenbeck process in quantum mechanics and the sub-quantum coherence effect

Third quantization is used in open quantum systems to construct a superoperator basis in which quadratic Lindbladians can be turned into a normal form. From it follows the spectral properties of the Lindbladian, including eigenvalues and eigenvectors. However, the connection between third quantization and the semiclassical representations usually employed to obtain the dynamics of open quantum systems remains opaque. We introduce an alternative basis for third quantization that bridges this gap between third quantization and the $Q$ representation by projecting the master equation onto a superoperator coherent-state basis. The equation of motion reduces to a multidimensional complex Ornstein-Uhlenbeck process.Third quantization is used in open quantum systems to construct a superoperator basis in which quadratic Lindbladians can be turned into a normal form. From it follows the spectral properties of the Lindbladian, including eigenvalues and eigenvectors. However, the connection between third quantization and the semiclassical representations usually employed to obtain the dynamics of open quantum systems remains opaque. We introduce an alternative basis for third quantization that bridges this gap between third quantization and the $Q$ representation by projecting the master equation onto a superoperator coherent-state basis. The equation of motion reduces to a multidimensional complex Ornstein-Uhlenbeck process.

arXiv:2408.11893Physical Review ANov 6, 20251 citation

Simulating Decoherence of a Nitrogen – Vacancy Centre Spin Qubit via Ornstein – Uhlenbeck Process

Alfaiz Fahrurrachman, Muhammad Aziz Majidi, Genko T. Genov +1 more

Abstract Owing to its remarkable optical properties and its ability to be controlled by microwave fields at room temperature, nitrogen-vacancy (NV) centre in diamond has been a promising platform for various nanotechnological applications, e.g. quantum sensing and magnetic resonance spectroscopy. The qubit associated with the NV centre ground state spin has been the key element for the realisation of such applications. Its coherence time determines the application performances, e.g. the sensitivity of the NV-qubit based quantum sensor. Due to unwanted and unavoidable interactions with noisy environment, the qubit undergoes decoherence that shortens its coherence time and hence reduces its application performance. Therefore, the investigation and mitigation of the decoherence of the NV qubit are of the utmost importance. Here, we simulate the qubit decoherence using Ornstein-Uhlenbeck process that is essential for designing a set of modulating control pulses to mitigate the effect.Abstract Owing to its remarkable optical properties and its ability to be controlled by microwave fields at room temperature, nitrogen-vacancy (NV) centre in diamond has been a promising platform for various nanotechnological applications, e.g. quantum sensing and magnetic resonance spectroscopy. The qubit associated with the NV centre ground state spin has been the key element for the realisation of such applications. Its coherence time determines the application performances, e.g. the sensitivity of the NV-qubit based quantum sensor. Due to unwanted and unavoidable interactions with noisy environment, the qubit undergoes decoherence that shortens its coherence time and hence reduces its application performance. Therefore, the investigation and mitigation of the decoherence of the NV qubit are of the utmost importance. Here, we simulate the qubit decoherence using Ornstein-Uhlenbeck process that is essential for designing a set of modulating control pulses to mitigate the effect.

Journal of Physics Conference SeriesMay 1, 20233 citations

Quantum Coherence and the Nonlinear Schrödinger Equation

David W. Brown, Katja Lindenberg, Bruce J. West

Springer series in solid-state sciencesJan 1, 19870 citations

Quantum Theory of Coherence

Springer eBooksOct 22, 20076 citations

Quantum chaos in atom optics: using phase noise to model continuous momentum and position measurement

Sigurd Dyrting, Gerard J Milburn

We study the effect of noise on the quantum nonlinear motion of a two-level atom in a laser standing wave. This system has recently been shown to exhibit dynamic localization in the atomic momentum. Noise is introduced through the phase of the standing wave, and has one of two forms: Weiner noise or Ornstein - Uhlenbeck noise. Using the theory of stochastic Hamiltonians we derive a master equation to describe the quantum mechanical evolution of the momentum statistics. We show that the Weiner noise process is then equivalent to a continuous measurement of the momentum of the atom, and the Ornstein - Uhlenbeck process describes a measurement of the position of the atom up to the period of the optical potential. We study the effect of noise when the classical dynamics shows global chaos.We study the effect of noise on the quantum nonlinear motion of a two-level atom in a laser standing wave. This system has recently been shown to exhibit dynamic localization in the atomic momentum. Noise is introduced through the phase of the standing wave, and has one of two forms: Weiner noise or Ornstein - Uhlenbeck noise. Using the theory of stochastic Hamiltonians we derive a master equation to describe the quantum mechanical evolution of the momentum statistics. We show that the Weiner noise process is then equivalent to a continuous measurement of the momentum of the atom, and the Ornstein - Uhlenbeck process describes a measurement of the position of the atom up to the period of the optical potential. We study the effect of noise when the classical dynamics shows global chaos.

Quantum and Semiclassical Optics Journal of the European Optical Society Part BJun 1, 199617 citations

Q

representation by projecting the master equation onto a superoperator coherent-state basis. The equation of motion reduces to a multidimensional complex Ornstein-Uhlenbeck process.