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Physical Review Letters

Coherent Control of Three-Level System Using Shaped Free Electrons

Anonymous, Jing Li, Yuhan Jiang, Yunquan Liu

Published Jul 8, 2026• 1 citation
Publisher

Abstract

Three-level systems exhibit quantum interference effects absent in two-level systems, making them important for quantum optics. Here, we study the coherent interaction of a Λ-type three-level system with free electrons shaped by optical near fields. By treating the electron train as a quantum drive, we show that the interplay between electron modulation and the three-level system's transition pathways induces tunable interference patterns. This interaction effectively realizes electron-mediated coherent population trapping. We identify a regime that enables complete population transfer between the two lower states and the preparation of a high-coherence superposition, manifested as dark states. In particular, these driven-dissipative steady states are independent of the initial state. Our Letter proposes shaped free electrons as a platform for steady-state coherent control of three-level systems, enabling atomic-scale state engineering.

DOI
10.1103/l2y4-tpzb

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Three-level systems exhibit quantum interference effects absent in two-level systems, making them important for quantum optics. Here, we study the coherent interaction of a Λ-type three-level system with free electrons shaped by optical near fields. By treating the electron train as a quantum drive, we show that the interplay between electron modulation and the three-level system's transition pathways induces tunable interference patterns. This interaction effectively realizes electron-mediated coherent population trapping. We identify a regime that enables complete population transfer between the two lower states and the preparation of a high-coherence superposition, manifested as dark states. In particular, these driven-dissipative steady states are independent of the initial state. Our Letter proposes shaped free electrons as a platform for steady-state coherent control of three-level systems, enabling atomic-scale state engineering.
Three-level systems exhibit quantum interference effects absent in two-level systems, making them important for quantum optics. Here, we study the coherent interaction of a Lambda-type three-level system with free electrons shaped by optical near fields. By treating the electron train as a quantum drive, we show that the interplay between electron modulation and the three-level system's transition pathways induces tunable interference patterns. This interaction effectively realizes electron-mediated coherent population trapping (CPT). We identify a regime that enables complete population transfer between the two lower states and the preparation of a high-coherence superposition, manifested as dark states. In particular, these driven-dissipative steady states are independent of the initial state. Our work proposes shaped free electrons as a platform for steady-state coherent control of three-level systems, enabling atomic-scale state engineering.
Atomic coherence and interference manifested by electromagentically induced transparency (EIT) and coherent population trapping (CPT) plays an important role in the current studies of atom-photon interactions and has found numerous applications in optical physics. EIT is created in a three-level atomic system by a coupling field and results in destructive interference between two excitation paths of a weak probe laser interacting with the atomic medium. This leads to suppressed linear absorption and rapidly varying atomic dispersion for the probe laser near the atomic resonance, which provides the platform for a variety of applications such as nonlinear optics at low light levels, slow light manipulation, and quantum state engineering for photons and atoms. Here we extend the simple three-level EIT system to more complicated and versatile configurations in a multi-level atomic system coupled by multiple laser fields. We show that with multiple excitation paths provided by different laser fields, phase-dependent quantum interference is induced: either constructive or destructive interference can be realized by varying the relative phases among the laser fields. Two specific examples are discussed. One is a three-level system coupled by bichromatic coupling and probe fields, in which the phase dependent interference between the resonant two-photon Raman transitions can be initiated and controlled. Another is a four-level system coupled by two coupling fields and two probe fields, in which a double-EIT configuration is created by the phase-dependent interference between three-photon and one-photon excitation processes. We analyze the coherently coupled multi-level atomic system and discuss the control parameters for the onset of constructive or destructive quantum interference. We describe two experiments performed with cold Rb atoms that can be approximately treated as the coherently coupled three-level and four-level atomic systems respectively. The experimental results show the phase-dependent quantum coherence and interference in the multi-level Rb atomic system, and agree with the theoretical calculations based on the coherently coupled three-level or four-level model system.
This work investigates the possibility of realizing coherent population trapping (CPT) in a two-electron three-level system with parallel spins. Making an analogy with solid-state physics, this study demonstrates that a V-type three-level system with two electrons can be described as a /spl Lambda/-type three-level system for one single hole. Cancellation of the probe field absorption is obtained when the hole is placed in the dark state. Alternatively, in terms of the two-electron V-type system, the CPT condition is realized when one electron is placed in the ground state and the other one in the bright combination of the excited states. In addition, when the electron-electron Coulomb repulsion is taken into account, it is shown that this technique offers the possibility of measuring, with subnatural resolution, some superposition-state matrix elements of the electron-electron correlation that due to their time dependent nature are inaccessible by standard measuring procedures.
In this thesis, we present work on coherent control of multilevelquantum systems in the strong field limit using shaped ultrafastlaser pulses. In recent years there have been numerous multiphotonabsorption experiments in two,three, and four-level atomic/molecularsystems and many are performed in the limit of weak fields whereperturbation theory is valid. Here, we describe a series ofexperiments aimed at exploring and understanding multiphotontransitions when the exciting field is strong and perturbationtheory breaks down. Our approach to strong field control utilizesboth parameterized scans of various pulse shapes and closed-looplearning control to identify a pulse shape that is optimal forpopulating a target quantum state. With this we will highlight thedifference between sequential population transfer and adiabaticrapid passage in multilevel systems with multiphoton couplingbetween levels. Additionally, we examine strong field control of afour-level atomic interferometer and show how interference in atarget state changes from resonant pathways in the frequency domainto time-domain interference via a singe path.Further, we use shaped femtosecond pulses to demonstrate aphenomenon in which a three-level atom becomes a modulator of anultrafast pulse. The results are based on a pump-probe scheme thatis very similar to Electromagnetically Induced Transparency (EIT).Important dynamics associated with a time-dependent coupling fieldare examined. Lastly, we extend previous work on two-photon drivensuperfluorescence from a shaped ultrafast drive laser and show howstimulated emission near threshold can turn modest coherent controlyields into essentially perfect discrimination between systems wherea control factor of about 104 is achieved between atomic andmolecular species.
The dynamics of an atomic few-level system can depend on the phase of driving fields coupled to the atom if certain conditions are satisfied. This is of particular interest to control interference effects, which can alter the system properties considerably. In this article, we discuss the mechanisms of such phase control and interference effects in an atomic three-level system in the Λ configuration, where the upper state spontaneously decays into the two lower states. The lower states are coupled by a driving field, which we treat as quantized. This allows for an interpretation on the single photon level for both the vacuum and the driving field. By analysing the system behaviour for a driving field initially in non-classical states with only a few Fock number states populated, we find that even though the driving field is coupled to the lower states only, it induces a multiplet of upper states. Then interference occurs independently in three-level subsystems in the V configuration, each formed by two adjacent upper states and a single dressed lower state.
A new scheme is suggested to manipulate the probe transitions (and hence the optical properties of atomic vapors) via double-control destructive and constructive quantum interferences. The influence of phase coherence between the two control transitions on the probe transition is also studied. The most remarkable feature of the present scheme is that the optical properties (absorption, transparency and dispersion) of an atomic system can be manipulated using this double-control multi-pathway interferences (multiple routes to excitation). It is also shown that a four-level system will exhibit a two-level resonant absorption because the two control levels (driven by the two control fields) form a dark state (and hence a destructive quantum interference occurs between the two control transitions). However, the present four-level system will exhibit electromagnetically induced transparency to the probe field when the three lower levels (including the probe level and the two control levels) form a three-level dark state. The present scenario has potential applications in new devices (e.g. logic gates and sensitive optical switches) and new techniques (e.g. quantum coherent information storage).