many-body rabi oscillations in rydberg atomic...

Quantum Optics Final Project

Many-body Rabi oscillations in Rydberg atomic ensembles

Huy Nguyen


April 17th, 2018


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


Rydberg Atoms

Tunable Interactions [1]

▪ Interaction strength over 12 orders of 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


Single atom qubits [1]

▪ Pro: Easier implementation

▪ Con: Slow manipulations of quantum state

Rydberg Mediated Quantum Gates


Ensemble qubits

▪ Pro: Strong atom-field coupling

▪ Con: Dependent on Rydberg blockade mechanism


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


Toy Model – 3 Site Lattice

Reflection symmetry imposed by open boundary condition [3]

Symmetric Subspace Reduction



Excitation dynamics in small lattices

Weak Interaction Strength

▪ Periodic beating

Strong Rydberg Interaction

▪ Coherent oscillations▪ No visible damping



Decoherence due to neighboring atoms

▪ Damped Rabi oscillations

10 Lattice Site Dynamics

Rich Excitation Dynamics

▪ Collapse and revival of Rydberg polariton



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 lightshift caused by doubly excited statesonto singly excited Rydberg states


Possible dephasing mechanisms

▪ Collisions

▪ Atomic motion

▪ Radiative decay

▪ Atom loss

▪ Stark shifts


Interaction-induced inhomogeneous lightshifts

Effective Hamiltonian to model decoherence:

Strategy:

▪ Consider uniform excitation Ω𝑖= Ω𝑗 = Ω

▪ Solve low dimensional Hilbert system analytically

▪ Perform spatial average of positiondependent light shifts across sample distribution


Two Dimensional Hilbert Space – Analytic Solutions

Collective states

Analytic expressions for coefficients


Effective Rabi Frequency


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)


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



Analytic expressions for averaged coefficients

Gaussian density distribution averaged:Airy and Airy prime functions

Uniform density distribution averaged : Gamma and Incomplete Gamma functions


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


Varying blockade ratio - Dephasing

+

-


Multi-excitation induced Stark shifts

Atom-Field Hamiltonian

[7] P. Berman

Wish to investigate the effect of multiple atoms in the intermediate 𝑝 state


3 Atom Collective State Amplitudes


Collective amplitudes

System of differential equations for collective amplitudes

Multiple p excitations causes effective damping of Rabi oscillation

[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)


Measure of Entanglement

Violation of Bell inequality

Overlap with Bell State

Increase in entanglement with more atoms and stronger Rydberg blockade


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.


Questions?


References


[2] S.-Y. Lan et al., Opt. Exp. 17, 13639 (2009)




[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.


Supplementary : Preparation Fidelity

many-body rabi oscillations in rydberg atomic...

Documents