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 ▪ Excitation dynamics in small lattices ▪ Decoherence mechanisms ▪ Multiply excited Rydberg states ▪ Intermediate P state excitations ▪ Generation of entanglement Quantum Optics Final Project
Rydberg Atoms Tunable Interactions [1] ▪ Interaction strength over 12 orders of magnitude Multiplexed Quantum Memory [2] ▪ Many applications in quantum information [1] M. Saffman, T. G. Walker, and K. Molmer, RMP 82 , 2313 (2010) Quantum Optics Final Project [2] S.-Y. Lan et al., Opt. Exp. 17 , 13639 (2009)
Rydberg Mediated Quantum Gates Single atom qubits [1] Ensemble qubits ▪ Pro: Easier implementation ▪ Pro: Strong atom-field coupling ▪ Con: Slow manipulations of ▪ Con: Dependent on Rydberg quantum state blockade mechanism Quantum Optics Final Project [1] M. Saffman, T. G. Walker, and K. Molmer, RMP 82 , 2313 (2010)
Excitation dynamics in small lattices Excitations driven by coherent laser: Interactions between excited states: Quantum Optics Final Project [3] G. Wu et al. / Physics Letters A 379 (2015) 143-148
Toy Model – 3 Site Lattice Reflection symmetry imposed by open boundary condition [3] Symmetric Subspace Reduction Quantum Optics Final Project [3] G. Wu et al. / Physics Letters A 379 (2015) 143-148
Excitation dynamics in small lattices Weak Interaction Strength ▪ Periodic beating Strong Rydberg Interaction ▪ Coherent oscillations ▪ No visible damping Quantum Optics Final Project [3] G. Wu et al. / Physics Letters A 379 (2015) 143-148
10 Lattice Site Dynamics Rich Excitation Dynamics ▪ Collapse and revival of Rydberg polariton Decoherence due to neighboring atoms ▪ Damped Rabi oscillations Quantum Optics Final Project [3] G. Wu et al. / Physics Letters A 379 (2015) 143-148
Many Body Rabi Oscillations Collective Dicke States Enhancement of Atom-Field Coupling We wish to model inhomogeneous light shift caused by doubly excited states onto singly excited Rydberg states Quantum Optics Final Project [4] Y. O. Dudin, L. Li, F. Bariani, and A. Kuzmich, Nat. Phys. 8 , 790 (2012)
Possible dephasing mechanisms ▪ Collisions ▪ Atomic motion ▪ Radiative decay ▪ Atom loss ▪ Stark shifts Quantum Optics Final Project
Interaction-induced inhomogeneous lightshifts Effective Hamiltonian to model decoherence: Strategy: ▪ Consider uniform excitation Ω 𝑗 = Ω 𝑘 = Ω ▪ Solve low dimensional Hilbert system analytically ▪ Perform spatial average of position dependent light shifts across sample distribution Quantum Optics Final Project
Two Dimensional Hilbert Space – Analytic Solutions Collective states Effective Rabi Frequency Analytic expressions for coefficients Quantum Optics Final Project [4] Y. O. Dudin, L. Li, F. Bariani, and A. Kuzmich, Nat. Phys. 8 , 790 (2012)
Probability Density Function – Uniform vs Gaussian Gaussian vs Uniform density sphere Probability density function for n-dimensional sphere with uniform density distribution [5] Probability density function for n-dimensional sphere with Gaussian density distribution Quantum Optics Final Project [5] Shu-Ju Tu and Ephraim Fishbach (2001)
Probability Density Function – Uniform vs Gaussian Gaussian vs Uniform Density Sphere Probability density function for 3-dimensional sphere with uniform density distribution Probability density function for 3-dimensional sphere with Gaussian density distribution Quantum Optics Final Project [5] Shu-Ju Tu and Ephraim Fishbach (2001)
Analytic expressions for averaged coefficients Uniform density distribution averaged : Gamma and Incomplete Gamma functions Gaussian density distribution averaged: Airy and Airy prime functions Quantum Optics Final Project
Estimating blockade parameters van der Waals coefficient [6] Effective Rabi frequency of two-photon transition 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) Quantum Optics Final Project [6] L.Beguin et al. PRL (2013)
Varying blockade ratio - Dephasing + - Quantum Optics Final Project
Multi-excitation induced Stark shifts Atom-Field Hamiltonian Wish to investigate the effect of multiple atoms in the intermediate 𝑞 state Quantum Optics Final Project [7] P. Berman
3 Atom Collective State Amplitudes Quantum Optics Final Project
Collective amplitudes System of differential equations for collective amplitudes Multiple p excitations causes effective damping of Rabi oscillation Quantum Optics Final Project [7] P. Berman
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) 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 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. Quantum Optics Final Project
Questions? 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. Quantum Optics Final Project
Supplementary : Preparation Fidelity Quantum Optics Final Project
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