.. _sphx_glr_api_gallery_quantum_open_systems:

Open quantum systems
--------------------

A qubit that leaks energy and phase into its environment: the Lindblad
master equation's :math:`T_1` relaxation and :math:`T_2` dephasing, and
the Monte Carlo wavefunction method that unravels the same dynamics into
individual jumping quantum trajectories.


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  <div id='sg-tag-list' class='sphx-glr-tag-list'></div>


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    <div class="sphx-glr-thumbcontainer" tooltip="A qubit coupled to a Markovian environment obeys Lindblad&#x27;s 1976 master equation. Here solve_lindblad evolves a qubit with energy-relaxation time T_1 and coherence time T_2 (collapse operators from t1_t2_collapse_operators): the excited population decays as e^{-t/T_1}, the precessing coherence \rho_{01} as e^{-t/T_2}, and the Bloch vector spirals inwards towards the ground state.">

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  .. image:: /api/gallery/quantum/open_systems/images/thumb/sphx_glr_plot_lindblad_master_equation_thumb.png
    :alt:

  :doc:`/api/gallery/quantum/open_systems/plot_lindblad_master_equation`

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      <div class="sphx-glr-thumbnail-title">The Lindblad master equation: T1 relaxation and T2 dephasing</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="Dalibard, Castin and Molmer (1992) showed that a Lindblad master equation can be unravelled into stochastic pure-state trajectories: each evolves under a non-Hermitian effective Hamiltonian and is interrupted by random quantum jumps. Here QuantumTrajectories simulates a resonantly driven, decaying two-level atom (resonance fluorescence). Single trajectories show Rabi flopping cut short by photon emissions; their average reproduces the Lindblad density matrix.">

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  .. image:: /api/gallery/quantum/open_systems/images/thumb/sphx_glr_plot_quantum_trajectories_thumb.png
    :alt:

  :doc:`/api/gallery/quantum/open_systems/plot_quantum_trajectories`

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      <div class="sphx-glr-thumbnail-title">Quantum trajectories: the Monte Carlo wavefunction method</div>
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    </div>


.. toctree::
   :hidden:

   /api/gallery/quantum/open_systems/plot_lindblad_master_equation
   /api/gallery/quantum/open_systems/plot_quantum_trajectories