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Physical Review A

Adiabatic population transfer by delayed laser pulses in multistate systems

Nikolay V. Vitanov

Published Sep 1, 1998• 71 citations
Publisher

Abstract

This paper analyzes the extension of the three-state process of stimulated Raman adiabatic passage to chainwise-connected multistate systems. A necessary condition for such a process is the existence of an adiabatic-transfer state, which connects adiabatically the initial state of the chain to its final state. Various counterintuitive pulse sequences are examined, in all of which the pulse that drives the last transition of the chain precedes the pulse driving the first transition, while the pulses driving the intermediate transitions may have different timings. The paper demonstrates some important qualitative differences and similarities between the systems with odd and even number of states. In the on-resonance case, an adiabatic-transfer state always exists for an odd number of states while it never exists for an even number of states. In the off-resonance case, however, the two types of systems behave in a very similar manner and the condition for existence of an adiabatic-transfer state is essentially the same. This condition, which imposes certain limitations on the laser parameters, is derived in a simple and compact form. It is also shown analytically that, besides by large detunings, the populations of the intermediate states (which are generally nonzero during the transfer) can be damped by large intermediate couplings. It is concluded that for an odd number of states, the optimal case is the on-resonance one, with equal and large intermediate couplings. For an even number of states, the optimal (off-resonance) case is when the intermediate couplings and the detunings have similar values. Various numerical examples of success and failure of multistate population transfer confirm the analytic conclusions.

DOI
10.1103/physreva.58.2295

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This paper analyzes the extension of the three-state process of stimulated Raman adiabatic passage to chainwise-connected multistate systems. A necessary condition for such a process is the existence of an adiabatic-transfer state, which connects adiabatically the initial state of the chain to its final state. Various counterintuitive pulse sequences are examined, in all of which the pulse that drives the last transition of the chain precedes the pulse driving the first transition, while the pulses driving the intermediate transitions may have different timings. The paper demonstrates some important qualitative differences and similarities between the systems with odd and even number of states. In the on-resonance case, an adiabatic-transfer state always exists for an odd number of states while it never exists for an even number of states. In the off-resonance case, however, the two types of systems behave in a very similar manner and the condition for existence of an adiabatic-transfer state is essentially the same. This condition, which imposes certain limitations on the laser parameters, is derived in a simple and compact form. It is also shown analytically that, besides by large detunings, the populations of the intermediate states (which are generally nonzero during the transfer) can be damped by large intermediate couplings. It is concluded that for an odd number of states, the optimal case is the on-resonance one, with equal and large intermediate couplings. For an even number of states, the optimal (off-resonance) case is when the intermediate couplings and the detunings have similar values. Various numerical examples of success and failure of multistate population transfer confirm the analytic conclusions.
We present explicit analytic expressions for adiabatic dressed states which, in suitable limits, produce complete population transfer between initial and final states of a four-state excitation chain without ever placing appreciable population into intermediate states. The population-transfer scheme is a generalization of the three-state stimulated Raman adiabatic passage that makes use of counterintuitive pulse sequences. We demonstrate analytically and numerically that the four-state system differs in a very significant qualitative way from previously studied N-state systems with odd N. In particular, we find that the presence of modest detuning from single-photon resonance is critical to the success of population transfer.
This paper discusses a generalization of stimulated Raman adiabatic passage (STIRAP) in which the single intermediate state is replaced by N intermediate states. Each of these states is connected to the initial state ${\ensuremath{\psi}}_{i}$ with a coupling proportional to the pump pulse and to the final state ${\ensuremath{\psi}}_{f}$ with a coupling proportional to the Stokes pulse, thus forming a parallel multi-\ensuremath{\Lambda} system. It is shown that the dark (trapped) state exists only when the ratio between each pump coupling and the respective Stokes coupling is the same for all intermediate states. We derive the conditions for existence of a more general adiabatic-transfer state that includes transient contributions from the intermediate states but still transfers the population from state ${\ensuremath{\psi}}_{i}$ to state ${\ensuremath{\psi}}_{f}$ in the adiabatic limit. We present various numerical examples for success and failure of multi-\ensuremath{\Lambda} STIRAP, which illustrate the analytic predictions. Our results suggest that in the general case of arbitrary couplings, it is most appropriate to tune the pump and Stokes lasers either just below or just above all intermediate states.
Ongoing work aimed at developing highly efficient methods of populating a chosen sublevel of an energy level highlights the need to understand off-resonant effects in coherent excitation. This motivated us to re-examine some aspects of the theory of coherent excitation in a three-state system with a view to obtaining algebraic expressions for off-resonant eigenvalues and eigenvectors. Earlier work gives simple closed-form expressions for the eigenvalues this system, expressions applying even when the system is not on two-photon resonance. We present here expressions of similar simplicity for the components of the normalised eigenvectors. The analytic properties of these components explain the observed sensitivity of the stimulated-Raman-adiabatic-passage process (STIRAP) to the condition of two-photon resonance. None of the eigenstates is ‘trapped’ or ‘dark’ unless the system is on two-photon resonance; off resonance, all states have nonzero projections on the unperturbed intermediate state. A simple argument shows that no dressed state can be adiabatically connected to both the unperturbed initial and final states when the system is off two-photon resonance. That is, adiabatic transfer from initial to final state requires that these be degenerate before and after the STIRAP pulse sequence, and this implies zero two-photon detuning. However, substantial transfer probabilities are observed experimentally for very small two-photon detunings. We show that such systems are characterised by very sharp avoided crossings of two eigenvalues, and that the observed population transfer can be understood as an effect of non adiabatic transitions occurring at the avoided crossings.
The technique of stimulated Raman adiabatic passage (STIRAP) is a highly efficient tool for coherent population transfer in a chainwise-connected three-state quantum system. It is widely accepted that the two-photon resonance between the two end states of the chain is a crucial condition for STIRAP. This assumption is indeed correct when the two driving fields, pump and Stokes, produce nearly equal couplings for their respective transitions. We show analytically, supported by numeric examples, that when the pump and Stokes couplings differ significantly, the two-photon population transfer profile is distorted and its center is shifted away from the two-photon resonance; hence, the optimal operation of STIRAP demands a two-photon detuning. We derive simple analytic estimates for the center and the width of the two-photon profile. The results are of potential importance in situations when the pump and Stokes fields are of different physical natures (e.g., laser and cavity fields) or when two-photon resonance is unwanted (e.g., in the presence of residual light).
We consider an adiabatic population transfer process that resembles the well-established stimulated Raman adiabatic passage. In our system, the states have nonzero angular momentums J , therefore, the coupling laser fields induce transitions between the magnetic sublevels of the states. In particular, we discuss the possibility of creating coherent superposition states in a system with coupling pattern J = 0 ⇔ 1 and 1 ⇔ 2. Initially, the system is in the J = 0 state. We show that by, applying two delayed overlapping laser pulses, it is possible to create any final superposition state of the magnetic sublevels |2, −2⟩, |2, 0⟩, |2, +2⟩. Moreover, we find that the relative phases of the applied pulses influence not only the phases of the final superposition state but also the probability amplitudes. We show that if we fix the shape and the time delay between the pulses, the final state space can be entirely covered by varying the polarizations and relative phases of the two pulses. Performing numerical simulations we find that our transfer process is nearly adiabatic for the whole parameter set.