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Quantum Optics Final Project
Many-body Rabi oscillations in Rydberg atomic ensembles
Huy Nguyen
Quantum Optics Final Project April 17th, 2018
Quantum Optics Final Project
Rydberg atomic ensembles Huy Nguyen Quantum Optics Final Project - - PowerPoint PPT Presentation
Rydberg atomic ensembles Huy Nguyen Quantum Optics Final Project - - PowerPoint PPT Presentation
Many-body Rabi oscillations in Rydberg atomic ensembles Huy Nguyen Quantum Optics Final Project April 17 th , 2018 Quantum Optics Final Project Outline Applications of Rydberg atoms in quantum information Many-body Rabi oscillations
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Quantum Optics Final Project
Rydberg Atoms
Tunable Interactions [1] ▪ Interaction strength over 12 orders
- f magnitude
[1] M. Saffman, T. G. Walker, and K. Molmer, RMP 82, 2313 (2010) [2] S.-Y. Lan et al., Opt. Exp. 17, 13639 (2009)
Multiplexed Quantum Memory [2] ▪ Many applications in quantum information
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Quantum Optics Final Project
Single atom qubits [1] ▪ Pro: Easier implementation ▪ Con: Slow manipulations of quantum state
Rydberg Mediated Quantum Gates
[1] M. Saffman, T. G. Walker, and K. Molmer, RMP 82, 2313 (2010)
Ensemble qubits ▪ Pro: Strong atom-field coupling ▪ Con: Dependent on Rydberg blockade mechanism
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Quantum Optics Final Project
Excitation dynamics in small lattices
Excitations driven by coherent laser: Interactions between excited states:
[3] G. Wu et al. / Physics Letters A 379 (2015) 143-148
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Quantum Optics Final Project
Toy Model – 3 Site Lattice
Reflection symmetry imposed by open boundary condition [3] Symmetric Subspace Reduction
[3] G. Wu et al. / Physics Letters A 379 (2015) 143-148
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Quantum Optics Final Project
Excitation dynamics in small lattices
Weak Interaction Strength ▪ Periodic beating Strong Rydberg Interaction ▪ Coherent oscillations ▪ No visible damping
[3] G. Wu et al. / Physics Letters A 379 (2015) 143-148
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Quantum Optics Final Project
Decoherence due to neighboring atoms ▪ Damped Rabi oscillations
10 Lattice Site Dynamics
Rich Excitation Dynamics ▪ Collapse and revival of Rydberg polariton
[3] G. Wu et al. / Physics Letters A 379 (2015) 143-148
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Quantum Optics Final Project
Many Body Rabi Oscillations
[4] Y. O. Dudin, L. Li, F. Bariani, and A. Kuzmich, Nat. Phys. 8, 790 (2012)
Collective Dicke States Enhancement of Atom-Field Coupling We wish to model inhomogeneous light shift caused by doubly excited states
- nto singly excited Rydberg states
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Quantum Optics Final Project
Possible dephasing mechanisms
▪ Collisions ▪ Atomic motion ▪ Radiative decay ▪ Atom loss ▪ Stark shifts
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Quantum Optics Final Project
Interaction-induced inhomogeneous lightshifts
Effective Hamiltonian to model decoherence: Strategy: ▪ Consider uniform excitation Ω𝑗= Ω𝑘 = Ω ▪ Solve low dimensional Hilbert system analytically ▪ Perform spatial average of position dependent light shifts across sample distribution
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Quantum Optics Final Project
Two Dimensional Hilbert Space – Analytic Solutions
Collective states Analytic expressions for coefficients
[4] Y. O. Dudin, L. Li, F. Bariani, and A. Kuzmich, Nat. Phys. 8, 790 (2012)
Effective Rabi Frequency
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Quantum Optics Final Project
Probability Density Function – Uniform vs Gaussian
Gaussian vs Uniform density sphere Probability density function for n-dimensional sphere with Gaussian density distribution Probability density function for n-dimensional sphere with uniform density distribution [5]
[5] Shu-Ju Tu and Ephraim Fishbach (2001)
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Quantum Optics Final Project
Probability Density Function – Uniform vs Gaussian
Gaussian vs Uniform Density Sphere Probability density function for 3-dimensional sphere with Gaussian density distribution Probability density function for 3-dimensional sphere with uniform density distribution
[5] Shu-Ju Tu and Ephraim Fishbach (2001)
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Quantum Optics Final Project
Analytic expressions for averaged coefficients
Gaussian density distribution averaged: Airy and Airy prime functions Uniform density distribution averaged : Gamma and Incomplete Gamma functions
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Quantum Optics Final Project
Estimating blockade parameters
van der Waals coefficient [6] Bounds for van der Waals shift Ratio characterizing blockade
[4] Y. O. Dudin, L. Li, F. Bariani, and A. Kuzmich, Nat. Phys. 8, 790 (2012) [6] L.Beguin et al. PRL (2013)
Effective Rabi frequency of two-photon transition
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Quantum Optics Final Project
Varying blockade ratio - Dephasing
+
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Quantum Optics Final Project
Multi-excitation induced Stark shifts
Atom-Field Hamiltonian
[7] P. Berman
Wish to investigate the effect of multiple atoms in the intermediate 𝑞 state
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Quantum Optics Final Project
3 Atom Collective State Amplitudes
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Quantum Optics Final Project
Collective amplitudes
System of differential equations for collective amplitudes Multiple p excitations causes effective damping
- f Rabi oscillation
[7] P. Berman
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Quantum Optics Final Project
Generation of Entanglement – CNOT Gate
Generating Bell State
- 1. Prepare two qubit input state:
- 2. Apply CNOT gate:
- 3. Output state is maximally entangled (ideal scenario)
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Quantum Optics Final Project
Measure of Entanglement
Violation of Bell inequality Overlap with Bell State Increase in entanglement with more atoms and stronger Rydberg blockade
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Quantum Optics Final Project
Summary
▪ Rydberg ensemble qubits allow for fast quantum state preparation and manipulation ▪ Several mechanisms lead to damping of Rabi oscillations ▪ Doubly excited Rydberg states ▪ Multiple intermediate P state excitations ▪ Breakdown of Rydberg blockade leads to reduced fidelity of quantum gate operations ▪ Combine both mechanisms as well as include additional effects such as atom loss and radiative decay.
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Quantum Optics Final Project
Questions?
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Quantum Optics Final Project
References
[1] M. Saffman, T. G. Walker, and K. Molmer, RMP 82, 2313 (2010) [2] S.-Y. Lan et al., Opt. Exp. 17, 13639 (2009) [3] G. Wu et al. / Physics Letters A 379 (2015) 143-148 [4] Y. O. Dudin, L. Li, F. Bariani, and A. Kuzmich, Nat. Phys. 8, 790 (2012) [5] Shu-Ju Tu and Ephraim Fishbach (2001) [6] L.Beguin et al. PRL (2013) [7] Paul R. Berman, V. S. (2011). Principles of Laser Spectroscopy and Quantum Optics. Princeton: Princeton University Press.
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Quantum Optics Final Project