quantum optics: shortcuts to adiabaticity · quantum simulation metrology essential: preparation,...
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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: [email protected]
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