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Physical Review A

Tunable Landau-Zener transitions using continuous- and chirped-pulse-laser couplings

Farrokh Sarreshtedari, Mehdi Hosseini

Published Mar 27, 2017• 17 citations
Publisher

Abstract

The laser coupled Landau-Zener avoided crossing has been investigated with an aim towards obtaining the laser source parameters for precise controlling of the state dynamics in a two-level quantum system. The conventional Landau-Zener equation is modified for including the interaction of the system with a laser field during a bias energy sweep and the obtained Hamiltonian is numerically solved for the investigation of the two-state occupation probabilities. We have shown that in the Landau-Zener process, using an additional laser source with controlled amplitude, frequency, and phase, the system dynamics could be arbitrarily engineered. This is while, by synchronous frequency sweeping of a chirped-pulse laser, the system could be guided into a resonance condition, which again gives the remarkable possibility for precise tuning and controlling of the quantum system dynamics.

DOI
10.1103/physreva.95.033834

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The laser coupled Landau-Zener avoided crossing has been investigated with an aim towards obtaining the laser source parameters for precise controlling of the state dynamics in a two-level quantum system. The conventional Landau-Zener equation is modified for including the interaction of the system with a laser field during a bias energy sweep and the obtained Hamiltonian is numerically solved for the investigation of the two-state occupation probabilities. We have shown that in the Landau-Zener process, using an additional laser source with controlled amplitude, frequency, and phase, the system dynamics could be arbitrarily engineered. This is while, by synchronous frequency sweeping of a chirped-pulse laser, the system could be guided into a resonance condition, which again gives the remarkable possibility for precise tuning and controlling of the quantum system dynamics.
We explore the control of the Landau-Zener (LZ) transition in NaI predissociation with low-intensity linearly and quadratically chirped femtosecond far-infrared laser pulses by solving the coupled time-dependent Schrödinger equations. We find that the LZ transition between the excited state and the ground state can be enhanced or be suppressed using a well-delayed control pulse with a proper linear or quadratic chirp. With instantaneously controlling the energy gap, the resonant population inversion induced by Rabi oscillation can facilitate or prohibit the molecular population transfer in the avoided-crossing region. This work provides a deep understanding of coherent control of LZ transition in molecular reaction with chirped femtosecond laser pulses.
Transition dynamics of a coupled two-particle quantum system is numerically investigated in a laser controlled Landau–Zener process. The effect of the laser parameters as well as the coupling strength of the particles on the Landau–Zener transition dynamics are investigated and discussed. It is shown that the coupling strength between the particles, which describes the ferromagnetic or antiferromagnetic behavior of the system, interestingly changes the uncoupled system transitions and introduces new intermediate states. The obtained results provide the required controlling parameters for optimal engineering of the quantum states.
The Landau--Zener (LZ) model describes a two-level quantum system that undergoes an avoided crossing. In the adiabatic limit, the transition probability vanishes. An auxiliary control field HCDH_\text{CD}HCD​ can be reverse-engineered so that the full Hamiltonian H0+HCDH_0 + H_\text{CD}H0​+HCD​ reproduces adiabaticity for all parameter values. Our aim is to construct a single control field H1H_1H1​ that drives an ensemble of LZ-type Hamiltonians with a distribution of energy gaps. H1H_1H1​ works best statistically, minimizing the average transition probability. We restrict our attention to a special class of H1H_1H1​ controls, motivated by HCDH_\text{CD}HCD​. We found a systematic trade-off between instantaneous adiabaticity and the final transition probability. Certain limiting cases with a linear sweep can be treated analytically; one of them being the LZ system with Dirac δ(t)δ(t)δ(t) function. Comprehensive and systematic numerical simulations support and extend the analytic results.
Abstract We have proposed and demonstrated a fast and robust method of population transfer between two quantum states using a quadratically chirped laser source. Numerically solving the time-dependent Schrödinger equation, transition probabilities have been obtained and the condition of the adiabatic passage is investigated. In this scheme, the wavelength of a laser source is quadratically swept in time to arbitrarily engineer the transition probabilities. The results show that complete and robust population transfer could be achieved by appropriate adjusting of the system parameters including the laser chirping parameter, the center frequency, and the coupling strength. Using this method, the time of the complete transition could be drastically decreased compared to the incorporation of the traditional linearly chirped laser.
Considering a temperature dependent two-level quantum system, we have numerically solved the Landau-Zener transition problem.The method includes the incorporation of temperature effect as a thermal noise added Schrödinger equation for the construction of the Hamiltonian.Here, the obtained results which describe the changes in the system including the quantum states and the transition probabilities are investigated and discussed.The results successfully describe the behavior of the transition probabilities by sweeping the temperature.
By driving a 3D transmon with microwave fields, we generate an effective avoided energy-level crossing. Then we chirp microwave frequency, which is equivalent to driving the system through the avoided energy-level crossing by sweeping the avoided crossing. A double-passage chirp produces Landau-Zener-Stückelberg-Majorana (LZSM) interference that agree well with the numerical results, especially with the initial state being an eigen-energy state in the center of an avoided level crossing. A time-resolved state tomography measurement is performed in the evolution of LZSM interference, showing an experimental evidence for the dynamical evolution of quantum state. Our method is fully applicable to other quantum systems that contain no intrinsic avoided level crossing, providing an alternative approach for quantum control and quantum simulation.