Multiparticle Landau-Zener problem: Application to quantum dots

Sinitsyn, Nikolai A.

doi:10.1103/physrevb.66.205303

Cited by 56 publications

(106 citation statements)

References 19 publications

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“…This result agrees with the continuum limit of the Demkov-Osherov S matrix [20,21] for a single level crossing a group of stationary levels. We next employ the single-particle S matrix (7) in the calculation of the many-body properties, taking as the initial state the filled Fermi sea.…”

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confidence: 81%

Coherent Particle Transfer in an On-Demand Single-Electron Source

2008

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Electron transfer from a localized state in a quantum dot into a ballistic conductor generally results in particle-hole excitations. We study this effect, considering a resonance level with time-dependent energy coupled to particle states in the Fermi sea. We find that, as the resonance level is driven through the Fermilevel, particle-hole excitations can be suppressed for certain driving protocols. In particular, such noiseless transfer occurs if the level moves with constant rapidity, its energy changing linearly with time. A scheme to study the coherence of particle transfer is proposed. DOI: 10.1103/PhysRevLett.101.196404 PACS numbers: 71.10.Pm, 03.65.Ud, 03.67.Hk, 73.50.Td Individual quantum states of light, supplied on demand by single-photon sources [1][2][3], are essential for current progress in manipulating and processing quantum information in quantum optics [4]. In particular, such sources are at the heart of secure transmission of quantum information by quantum cryptography [5], and of quantum teleportation [6]. An extension of these techniques to electron systems would be crucial for the inception of fermionbased quantum information processing [7,8].Elements of solid state electron optics, such as linear beam splitters [9,10] and interferometers [11], have been known for a while, but an on-demand electron source was demonstrated only recently [12]. In the experiment [12] a localized state in a quantum dot, tunnel-coupled to a ballistic conductor (a quantum Hall edge channel), was charged and discharged by modulation of its energy induced by a periodic voltage on the gate, leading to a sequence of quantized single-electron current pulses [13].Yet, the nearly perfect quantization of current pulses achieved in [12] does not guarantee full quantum coherence. In a fully coherent pulse, the injected electron occupies a prescribed quantum state without particle-hole pairs excited from the Fermi sea. However, as the particle or hole density of states is finite at low energy a generic perturbation applied to a Fermi system can create multiple pairs. This process is more disruptive than related process for photon sources (e.g., phonon emission), as these particlehole pairs occur in the same channel as the desired particle. Avoiding such excitations constrains the protocol for generating coherent pulses.To study the coherence of particle transfer, we use an exact time-dependent scattering matrix, generalizing the Breit-Wigner theory of resonance scattering to arbitrary time dependence of the localized state energy EðtÞ. Applying this approach to the many-body evolution of a Fermi sea coupled to a localized state with driven energy, we find that for linear driving EðtÞ ¼ ct, excitation creation is fully inhibited. The harmonic driving used in [12] is well approximated by this linear model if electron release and capture occur well within each half-period, as shown in Fig. 1(a). For such clean protocols entanglement between the injected particle and the Fermi sea is totally suppressed by Pauli blocking of m...

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confidence: 81%

Coherent Particle Transfer in an On-Demand Single-Electron Source

2008

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“…Despite a number of fully solvable multistate LZ models has been known, all such models describe relatively simple situations, such as interactions of many uncoupled to each other levels with a single level [21,23]. Many known solvable cases are, in fact, reducible in the sense that they can be decoupled into a set of independent Demkov-Osherov, bow-tie, or two-state LZ models by applying simple well-characterized symmetry transformations [24]. Only recently, conditions of integrability, which we discussed in section 3B, have been used by one of us to uncover a few more relatively small-size solvable models [27,28].…”

Section: Discussionmentioning

confidence: 99%

“…Some of the multistate LZ models have been already studied with the purpose to obtain transition probabilities between diabatic states [21][22][23][24][25][26][27][28]. For example, the model (7) is a special case of the exactly solvable Demkov-Osherov model [21].…”

Section: Driven Tavis-cummings Model As a Multistate Landau-zenermentioning

confidence: 99%

Solvable multistate model of Landau-Zener transitions in cavity QED

Sinitsyn

2016

Phys. Rev. A

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We consider the model of a single optical cavity mode interacting with two-level systems (spins) driven by a linearly time-dependent field. When this field passes through values at which spin energy level splittings become comparable to spin coupling to the optical mode, a cascade of Landau-Zener (LZ) transitions leads to co-flips of spins in exchange for photons of the cavity. We derive exact transition probabilities between different diabatic states induced by such a sweep of the field.

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“…Therefore, only special cases are well understood, such as the four-state sector (S = 3/2), and the case of arbitrary S but specific initial conditions at t = −∞: with either |a n | 2 = δ n1 or |a n | 2 = δ nN . Any solvable MLZ model can be used to construct more complex ones by "populating" the original model with noninteracting fermions or bosons [1,17,26]. An example of such a composite model is shown in Fig.…”

Section: Bipartite Modelsmentioning

confidence: 99%

“…This article continues the series of publications [1][2][3][4][5] about exact results in the MLZ theory [6]. This theory deals with explicitly time-dependent Schrödinger equations of the form…”

Section: Introductionmentioning

confidence: 99%

Multistate Landau-Zener models with all levels crossing at one point

Sun

Chernyak

et al. 2017

Phys. Rev. A

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We discuss common properties and reasons for integrability in the class of multistate Landau-Zener (MLZ) models with all diabatic levels crossing at one point. Exploring the Stokes phenomenon, we show that each previously solved model has a dual one, whose scattering matrix can be also obtained analytically. For applications, we demonstrate how our results can be used to study conversion of molecular into atomic Bose condensates during passage through the Feshbach resonance, and provide purely algebraic solutions of the bowtie and special cases of the driven Tavis-Cummings model (DTCM).

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Multiparticle Landau-Zener problem: Application to quantum dots

Cited by 56 publications

References 19 publications

Coherent Particle Transfer in an On-Demand Single-Electron Source

Coherent Particle Transfer in an On-Demand Single-Electron Source

Solvable multistate model of Landau-Zener transitions in cavity QED

Multistate Landau-Zener models with all levels crossing at one point

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