quantum optics: shortcuts to adiabaticity · quantum simulation metrology essential: preparation,...

Dr. Andreas Ruschhaupt

Quantum Optics:

Shortcuts to Adiabaticity

Room 216AEmail: aruschhaupt@ucc.ie

MetrologyQuantum Simulation

Essential: Preparation, control and manipulation of quantum stateswith high fidelity and in a fast and robust way

Quantum InformationProcessing

Quantum Technology

Dr. Andreas Ruschhaupt, Shortcuts to Adiabaticity in Quantum Optics, p. 2

Shortcuts to Adiabaticity

Important:No excitations at the end!

Transport of an atom in a harmonic trap (e.g. an optical trap):

Dr. Andreas Ruschhaupt, Shortcuts to Adiabaticity in Quantum Optics, p. 3

Shortcuts to Adiabaticity

Transport of an atom in a harmonic trap (e.g. an optical trap):

Possibility: Do it slow:Adiabatic Transport

Adiabatic Theorem in Quantum Mechanics:

The desired final ground state will be exactly achievedif the trap will be moved infinitely slow.

Dr. Andreas Ruschhaupt, Shortcuts to Adiabaticity in Quantum Optics, p. 4

Shortcuts to Adiabaticity

Adiabatic transport:

Example: duration of transport: t = 4000 ms

Dr. Andreas Ruschhaupt, Shortcuts to Adiabaticity in Quantum Optics, p. 5

Shortcuts to Adiabaticity

Adiabatic transport:

Example: duration of transport: t = 4000 ms

Dr. Andreas Ruschhaupt, Shortcuts to Adiabaticity in Quantum Optics, p. 5

Advantage: Very robustDisadvantage: Very slow

Adiabatic Schemes:

Shortcuts to Adiabaticity

Adiabatic transport:

Example: duration of transport: t = 100 ms

Dr. Andreas Ruschhaupt, Shortcuts to Adiabaticity in Quantum Optics, p. 6

Advantage: Very robustDisadvantage: Very slow

Adiabatic Schemes:

Shortcuts to Adiabaticity

Adiabatic transport:

Example: duration of transport: t = 100 ms

Dr. Andreas Ruschhaupt, Shortcuts to Adiabaticity in Quantum Optics, p. 6

Advantage: Very robustDisadvantage: Very slow

Adiabatic Schemes:

Shortcut to Adiabaticity

Goal: New Methods for a fast and stable manipulation of atomic states

Shortcuts to Adiabaticity

Example: Shortcut: duration of transport: t = 100 ms

Fast and Stable

Dr. Andreas Ruschhaupt, Shortcuts to Adiabaticity in Quantum Optics, p. 7

Shortcut to Adiabaticity

Goal: New Methods for a fast and stable manipulation of atomic states

Shortcuts to Adiabaticity

Example: Shortcut: duration of transport: t = 100 ms

Fast and Stable Transport in 1 dimension

Dr. Andreas Ruschhaupt, Shortcuts to Adiabaticity in Quantum Optics, p. 7

Project 1

Dr. Andreas Ruschhaupt, Shortcuts to Adiabaticity in Quantum Optics, p. 8

Project 1Shortcuts for Trap Transports along Curved Lines

(Numerical, long or short)

Question: How about transport of traps along curved lineswithout excitations????

- resonant pulses (pi, pi/2, etc…)

fast but unstable

- adiabatic passage methods (RAP, STIRAP..)

robust but slow

In general we would like fast & robust processes

=> speeded-up adiabatic methods

Internal State Control

Two major routes to control internal state(for example population inversion 1 -> 2):

Goal: Manipulate the internal state of cold atoms

Dr. Andreas Ruschhaupt, Shortcuts to Adiabaticity in Quantum Optics, p. 8

Shortcuts to Internal State Manipulation

ExcitationProbability:

Example of Pi Pulse(green, dashed line)

Shortcut pulse(blue, dashed-dotted line)

(blue, dashed line)

(red, solid line)

)(t∆∆∆∆

RΩΩΩΩ

Shortcut to Adiabatic State Transfer:

• based on Invariants and Inverse Engineering

• speeded-up Rapid Adiabatic Passage:perfect population transfer in arbitrarily short, finite time

Dr. Andreas Ruschhaupt, Shortcuts to Adiabaticity in Quantum Optics, p. 9

Quantum InformationProcessing

Quantum Algorithms

Dr. Andreas Ruschhaupt, Shortcuts to Adiabaticity in Quantum Optics, p. 9

Project 2

Adiabatic Quantum Computing

Project 2Understanding of standard quantum algorithms

Determine the essential control operations and potential for speed-up (long or short)

Project 3 (Demanding/Interesting)

Dr. Andreas Ruschhaupt, Shortcuts to Adiabaticity in Quantum Optics, p. 10

Ref.: A. Kiely et. al., arXiv:1609.04272

Effect of Poisson Noise on Adiabatic Processes (Further examples

Hamiltonian with classical noise:

Master equation:

Project 4

Dr. Andreas Ruschhaupt, Shortcuts to Adiabaticity in Quantum Optics, p. 11

Ref.: S. Martinez-Garaot et. al., arXiv:1609.01887

Question: Trap deformation?

Change of Trap geometry:

, ~()

Technique: Fast-forward approach (inverting the Schrödinger equation)

ℏ

, = −

ℏ

∆ , + , ,

Projects (all short or long)

Project 3: Effect of Poisson noise on adiabaticity (Further examples)

The project will require analytical calculations as well as numerical calculations with Mathematica. Interesting/demanding project

Project 1: Shortcuts for transport along curved lines

The project will require analytical calculations as well as numerical solutions of the Schrödinger equation on a graphics processing unit (GPU).

Project 2: Quantum algorithmsThe project will require literature work, analytical calculations as well as numerical calculations with Mathematica.

Project 4: Trap deformation via Fast-forward Techniques

The project will require analytical calculations as well as numerical calculations with Mathematica.

Project 5: ???? (Very interesting/very difficult)

Dr. Andreas RuschhauptRoom 216A

Email: aruschhaupt@ucc.ie

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