Quantum Optics Final Project - PDF document

Quantum Optics Final ProjectMany-body
Quantum Optics Final ProjectMany-body Rabi oscillations in Rydberg atomic ensemblesHuy NguyenQuantum Optics Final ProjectApril 17th, 2018Quantum Optics Final ProjectOutline▪Applications of Rydberg atoms in quantum information

▪Many-body Rabi oscillations▪E
▪Many-body Rabi oscillations▪Excitation dynamics in small lattices▪Decoherence mechanisms▪MultiplyexcitedRydbergstates▪IntermediatePstateexcitations▪Generation of entanglementQuantum Optics Final ProjectR

ydberg AtomsTunable Interactions [1]â
ydberg AtomsTunable 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 Me

mory [2]▪Many applications in quant
mory [2]▪Many applications in quantum information Quantum Optics Final ProjectSingle atom qubits[1]▪Pro: Easier implementation▪Con: Slow manipulations of quantum stateRydberg Mediated Quantum Gates[1] M. Saffman, T. G. Wa

lker, and K. Molmer, RMP 82, 2313 (2
lker, and K. Molmer, RMP 82, 2313 (2010)Ensemble qubits▪Pro: Strong atom-field coupling▪Con: Dependent on Rydberg blockade mechanismQuantum Optics Final ProjectExcitation dynamics in small latticesExcitations driven by coher

ent laser:Interactions between excited
ent laser:Interactions between excited states:[3] G. Wu et al. / Physics Letters A 379 (2015) 143-148Quantum Optics Final ProjectToy Model –3 Site LatticeReflection symmetry imposed by open boundary condition [3]Symmetric Subsp

ace Reduction[3] G. Wu et al. / Physic
ace Reduction[3] G. Wu et al. / Physics Letters A 379 (2015) 143-148Quantum Optics Final ProjectExcitation dynamics in small latticesWeak Interaction Strength▪Periodic beatingStrong Rydberg Interaction▪Coherent oscillations▪

No visible damping[3] G. Wu et al. /
No visible damping[3] G. Wu et al. / Physics Letters A 379 (2015) 143-148Quantum Optics Final ProjectDecoherence due to neighboring atoms▪Damped Rabi oscillations10 Lattice Site DynamicsRich Excitation Dynamics▪Collapse and re

vival of Rydberg polariton[3] G. Wu e
vival of Rydberg polariton[3] G. Wu et al. / Physics Letters A 379 (2015) 143-148Quantum Optics Final ProjectMany Body Rabi Oscillations[4] Y. O. Dudin, L. Li, F. Bariani, and A. Kuzmich, Nat. Phys.8, 790 (2012)Collective D

ickeStatesEnhancement of Atom-Field
ickeStatesEnhancement of Atom-Field CouplingWewishtomodelinhomogeneouslightshiftcausedbydoublyexcitedstatesontosinglyexcitedRydbergstatesQuantum Optics Final ProjectPossible dephasing mechanisms▪Collisions▪Atomic

motion▪Radiative decay▪Atomlo
motion▪Radiative decay▪Atomloss▪Stark shiftsQuantum Optics Final ProjectInteraction-induced inhomogeneous lightshiftsEffective Hamiltonian to model decoherence:Strategy: ▪Consider uniform excitation Ω௜=Ω௝

=Ω▪Solve low dimensional Hilbert
=Ω▪Solve low dimensional Hilbert system analytically▪Performspatialaverageofpositiondependent light shifts across sample distributionQuantum Optics Final ProjectTwo Dimensional Hilbert Space –Analytic SolutionsCollect

ive statesAnalytic expressions for coef
ive statesAnalytic expressions for coefficients[4] Y. O. Dudin, L. Li, F. Bariani, and A. Kuzmich, Nat. Phys.8, 790 (2012)Effective Rabi FrequencyQuantum Optics Final ProjectProbability Density Function –Uniform vs Gaussian

Gaussian vs Uniform density sphereProba
Gaussian vs Uniform density sphereProbability 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)Quantum Optics
Ephraim Fishbach(2001)Quantum Optics Final ProjectProbability Density Function –Uniform vs GaussianGaussian vs Uniform Density SphereProbability density function for 3-dimensional sphere with Gaussian density distribution Probabi

lity density function for 3-dimensiona
lity density function for 3-dimensional sphere with uniform density distribution [5] Shu-Ju Tu and Ephraim Fishbach(2001)Quantum Optics Final ProjectAnalytic expressions for averaged coefficientsGaussian density distribution averag

ed:Airy and Airy prime functionsUnifor
ed:Airy and Airy prime functionsUniform density distribution averaged : Gamma and Incomplete Gamma functionsQuantum Optics Final ProjectEstimating blockade parametersvan der Waals coefficient [6]Bounds for van der Waals shiftRatio

characterizing blockade[4] Y. O. Dudi
characterizing blockade[4] Y. O. Dudin, L. Li, F. Bariani, and A. Kuzmich, Nat. Phys.8, 790 (2012)[6] L.Beguinet al. PRL (2013)Effective Rabi frequency of two-photon transitionQuantum Optics Final ProjectVarying blockade ra

tio -Dephasing+-Quantum Optics Fina
tio -Dephasing+-Quantum Optics Final ProjectMulti-excitation induced Stark shiftsAtom-Field Hamiltonian[7] P. BermanWish to investigate the effect of multiple atoms in the intermediate �state Quantum Optics Final

Project3 Atom Collective State Amplitu
Project3 Atom Collective State AmplitudesQuantum Optics Final ProjectCollective amplitudesSystem of differential equations for collective amplitudesMultiple p excitations causes effective damping of Rabi oscillation[7] P. BermanQuan

tum Optics Final ProjectGeneration of E
tum Optics Final ProjectGeneration of Entanglement –CNOT GateGenerating Bell State1. Prepare two qubit input state:2. Apply CNOT gate:3. Output state is maximally entangled (ideal scenario)Quantum Optics Final ProjectMeasure of Enta

nglementViolationofBellinequalityO
nglementViolationofBellinequalityOverlap with Bell StateIncrease in entanglement with more atoms and stronger Rydberg blockadeQuantum Optics Final ProjectSummary▪Rydberg ensemble qubits allow for fast quantum state preparation a

nd manipulation▪Several mechanisms l
nd 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 operation

s▪Combine both mechanisms as well as
s▪Combine both mechanisms as well as include additional effects such as atom loss and radiative decay.Quantum Optics Final ProjectQuestions?Quantum Optics Final ProjectReferences[1] M. Saffman, T. G. Walker, and K. Molmer, RMP 8

2, 2313 (2010)[2]S.-Y. Lan et al.
2, 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 Ephr

aim Fishbach(2001)[6] L.Beguinet al
aim Fishbach(2001)[6] L.Beguinet al. PRL (2013)[7] Paul R. Berman, V. S. (2011). Principles of Laser Spectroscopy and Quantum Optics.Princeton: Princeton University Press.Quantum Optics Final ProjectSupplementary : Preparation Fide