scholarly journals Information Geometric Perspective on Off-Resonance Effects in Driven Two-Level Quantum Systems

2020 ◽  
Vol 2 (1) ◽  
pp. 166-188 ◽  
Author(s):  
Carlo Cafaro ◽  
Steven Gassner ◽  
Paul M. Alsing
Keyword(s):  
Resonance Condition ◽  
Transition Probability ◽  
Geometric Analysis ◽  
Quantum Systems ◽  
Time Dependent ◽  
Population Transfer ◽  
Resonance Effects ◽  
Hamiltonian Models ◽  
Exactly Solvable ◽  
Geodesic Paths

We present an information geometric analysis of off-resonance effects on classes of exactly solvable generalized semi-classical Rabi systems. Specifically, we consider population transfer performed by four distinct off-resonant driving schemes specified by su 2 ; ℂ time-dependent Hamiltonian models. For each scheme, we study the consequences of a departure from the on-resonance condition in terms of both geodesic paths and geodesic speeds on the corresponding manifold of transition probability vectors. In particular, we analyze the robustness of each driving scheme against off-resonance effects. Moreover, we report on a possible tradeoff between speed and robustness in the driving schemes being investigated. Finally, we discuss the emergence of a different relative ranking in terms of performance among the various driving schemes when transitioning from on-resonant to off-resonant scenarios.

scholarly journals Exactly solvable time-dependent pseudo-Hermitian su(1,1) Hamiltonian models

2018 ◽  
Vol 98 (3) ◽  
Author(s):  
R. Grimaudo ◽  
A. S. M. de Castro ◽  
M. Kuś ◽  
A. Messina
Keyword(s):  
Time Dependent ◽  
Hamiltonian Models ◽  
Exactly Solvable

OPTIMALLY CONTROLLED VIBRATIONAL POPULATION TRANSFER IN A DIATOMIC QUANTUM SYSTEM

2009 ◽  
Vol 08 (01) ◽  
pp. 157-180 ◽  
Author(s):  
PRAVEEN KUMAR ◽  
SITANSH SHARMA ◽  
HARJINDER SINGH
Keyword(s):  
Iterative Method ◽  
Quantum System ◽  
Quantum Control ◽  
Vibrational Excitation ◽  
Transition Probability ◽  
Dipole Approximation ◽  
Time Dependent ◽  
Population Transfer ◽  
Initial State ◽  
Vibrational Population

A time-dependent formulation of quantum control is employed to investigate optimally controlled vibrational population transfer in a diatomic quantum system. The problem of finding the optimal laser field needed to achieve a specific quantum transition from an initial state to the desired target goal is formulated using an iterative method and the conjugate gradient method (CGM). The time-dependent Schrödinger equation is solved with interaction of laser radiation with matter included within a dipole approximation in the Hamiltonian. Appropriate boundary conditions are chosen for the evolution problem. The control objective is chosen as the value of transition probability from an initial state to a target state. A comparison is made between the results obtained using the iterative method and the CGM for optimization. Finally, quantum bits are encoded using the vibrational states of the diatomic in the regime of low-vibrational excitation.

PERFECT POPULATION TRANSFER IN PULSE-DRIVEN QUANTUM CHAINS

2010 ◽  
Vol 09 (05) ◽  
pp. 847-860 ◽  
Author(s):  
XIN CHEN ◽  
YAOXIONG WANG ◽  
YUNJIAN GE ◽  
JUNHUI SHI ◽  
HERSCHEL RABITZ ◽  
...  
Keyword(s):  
Quantum Dynamics ◽  
Nearest Neighbor ◽  
Control Strategies ◽  
Quantum Systems ◽  
Time Dependent ◽  
Population Transfer ◽  
Finite Dimensional ◽  
Analysis Technique ◽  
Quantum Chain ◽  
Multi Level

The quantum dynamics of a pulse-driven finite-dimensional quantum chain with only nearest-neighbor coupling is studied. We extend the concept of Rabi oscillations from two-level quantum systems to the multi-level quantum chains. The time-dependent quantum dynamics and solutions producing perfect population transfer are obtained for up to five-level quantum chains. The Gröbner basis analysis technique is used to generalize the results and get all analytical solutions for perfect population transfer. Explicit formulas for the solutions up to nine levels are presented. These results could be used to design control strategies for general finite-dimensional quantum systems.

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