Disentanglement in two qubit system subjected to dissipative
Disentanglement in two qubit system subjected to dissipative environment : Exact analysis Misbah Qurban Supervisor: Dr. Manzoor Ikram Pakistan Institute of Engineering and Applied Sciences National Institute of Lasers and Optronics International Scientific Spring 2016
2 Outline Ø Objectives Ø Single Atom Dynamics Ø Entanglement Ø Quantifiying Entanglement Ø Markovian Process Ø Non Markovian Process Ø Entanglement dynamics in Structured reservoir Ø Conclusion
3 Objectives • To Investigate the entanglement dynamics of close and separated atomic systems under nonmarkovian coupling • To enhance and prolong the entanglement in different environments
4 LOCAL DYNAMICS Two-level system coupled to vacuum System Ia> Ib> Reservoir (Vacuum) In the spontaneous decay of two-level atom in vacuum under Markovian approximation
5 Quantum Entanglement A quantum mechanical phenomenon in which the quantum states of two or more objects have to be described with reference to each other, even though the individual objects may be spatially separated. This leads to correlations between observable properties of the systems. Einstein called this “Spooky action at a distance”.
6 Entangled and separable states For separable state Example For entangled state Example
7 Quantitative measurement of entanglement (1) Concurrence λi’s eigenvalues unentangled states maximally entangled states partially entangled states W. K. Wooters, Phys. Rev. Lett. 80, 2245 (1998)
8 Quantitative measurement of entanglement (2) Negativity λi’s (3) Von- Neumann Entropy eigenvalues
9 System environment interaction Markovian Process Nonmarkovian Proce
10 Markovian Process Weak coupling process No feedback Memory effects are negligible Non Markovian Process strong coupling process feedback Memory effects are not negligible Short correlation time No restoration of superposition Flow of energy and information from the system to the environment can be momentarily reversed Recoherrence and restoration of lost superposition
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12 • Leaky cavities • Lorentenzian Spectral density
13 Model The Hamiltonian of the system in interaction picture is Approximations • Rotating wave approximation • Dipole approximation
14 Single atom dynamics in a leaky cavity The field inside the cavity is Atom =spectral width of field distribution = reservoir correlation time In strong coupling regime
15 Quantum theory of damping System reservoir interaction Density matrix for system Using Markove and Born approximation
16 Single atom dynamics in a leaky cavity Wave function of the system The dynamics obeys The correlation function is The decay rate for non markovian system For markovian coupling
17 Entanglement Dynamics in structured reservoir Equation of motion for the reduced density matrix assuming
18 using the basis The X-Matrix Entanglement dynamics for X type density matrix where
19 The matrix elements are determined from the master equation are
20 Dynamics of the state asymptotic decay and sudden death of entanglement (SDE) when is the spontaneous decay of two-level atom
21 Dynamics of the state Markovian dynamics Non Markovian dynamics
22 Case I: The initial state Markovian dynamics Non markovian dynamics maximum amount of entanglement when mixing a=0
23 Case II: Markovian dynamics Non markovian dynamics
24 Case III: Markovian dynamics Non markovian dynamics
25 Case IV: Markovian dynamics Non markovian dynamics
26 Conclusion • The dynamics in strong coupling regime is modified • Dynamics are slow • Sudden death time is delayed in each case • Shows oscillatory behavior due to the feedback from the environment
27 Publications • Misbah Qurban, Rabia Tahira, Rameez-ul- Islam and Manzoor Ikram “Disentanglement in a two qubit system subjected to dissipative environment: Exact analysis” Optics Communications 366, (2016) 285 -290. • Misbah Qurban, Tasawar Abbas, Rameez-ul- Islam and Manzoor Ikram “Quantum Teleportation of High-Dimensional Atomic Momenta State". Int J Theor Phys. DOI 10. 1007/s 10773 -016 -2930 -1 • Tasawar Abbas, Misbah Qurban, Rameez-ul- Islam and Manzoor Ikram. “Engineering distant cavity fields entanglement through Bragg diffraction of neutral atoms” Optics Communications 355, (2015)575 -579
28 ! ! ! Th k n a u o y
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