Landau-Zener-Stückelberg Interferometry of a Single Electronic Spin in a Noisy Environment

Huang, Pu; Zhang, Jingwei; Fang, Fang; Kong, Xinggong; Xu, Xiangkun; Ju, Chenyong; Du, Jiangfeng

doi:10.1103/physrevx.1.011003

Cited by 64 publications

(81 citation statements)

References 32 publications

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“…The combination of the ν 2 and the α-dependences allows in principle an initial nuclear spin temperature to be determined for each isotope. In practice, these temperatures are not significantly different to within the random error 11 and we take a common temperature for simplicity.The overall conclusion is that frequency-swept NMR enables the determination of all key parameters of the nuclear spins even at the single quantum dot level: the chemical composition, the effective temperatures and the quadrupole frequency distribution of each isotope.As an outlook, we note that a sweep adiabatic for |∆m = 1| but sudden for |∆m = 2| can be used to produce highly non-thermal distributions of the spin states, boosting the NMR signal of the central transitions.Also, at an intermediate sweep rate, a superposition of the spin states is created with a chirped NMR pulse, and back-and-forth frequency sweeps result in quantum interferences, the Stückelberg oscillations 18,[28][29][30][31] .This experiment represents the ideal springboard to explore quantum coherence in a complex nuclear spin ensemble using multiple chirped pulses. …”

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Manipulation of the nuclear spin ensemble in a quantum dot with chirped magnetic resonance pulses

et al. 2014

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The nuclear spins in nano-structured semiconductors play a central role in quantum applications [1][2][3][4] . The nuclear spins represent a useful resource for generating local magnetic 5 fields but nuclear spin noise represents a major source of dephasing for spin qubits 2,3 . Controlling the nuclear spins enhances the resource while suppressing the noise. Nuclear magnetic resonance (NMR) techniques are challenging: the group-III and group-V isotopes have large spins with widely different gyromagnetic-ratios; in strained material there are large atom-dependent quadrupole-shifts 6 ;nano-scale NMR is hard to detect 7,8 . We report NMR on 100, 000 nuclear spins of a quantum dot using chirped radio-frequency pulses. Following polarization, we demonstrate a reversal of the nuclear spin. We can flip the nuclear spin back-and-forth a hundred times. We demonstrate that chirped-NMR is a powerful way of determining the chemical composition, the initial nuclear spin temperatures and quadrupole frequency distributions for all the main isotopes. The key observation is a plateau in the NMR signal as a function of sweep-rate: we achieve inversion at the first quantum transition for all isotopes simultaneously. These experiments represent a generic technique for manipulating nano-scale inhomogeneous nuclear spin ensembles and open the way to probe the coherence of such mesoscopic systems.NMR signals can be boosted by polarizing the nuclei. This is particularly beneficial on the nano-scale where NMR signals are invariably small and hard to detect. The nuclear spins in a self-assembled quantum dot can be polarized optically by exploiting the hyperfine interaction with an electron spin 3,5 . Extremely long-lived polarizations 4,9-11 up to about 50% have been achieved. The nuclear spin polarization results in a shift of the optical resonance, the Overhauser shift, facilitating its sensitive detection 5 . These features have enabled the observation of isotope-selective NMR of the nuclear spins associated with strain-free GaAs quantum dots 12,13 . Self-assembled quantum dots, attractive for single photon generation and opticallycontrolled spin qubits 2 , have highly inhomogeneous nuclear spins 5,[14][15][16] Here we use chirped NMR pulses. The main concept is that by sweeping over a large frequency range, the pulse addresses each nuclear spin at some point. For a spin-1 2 nucleus, a 2-level system, the Hamiltonian in the rotating frame is,where h is the Planck constant, I the nuclear spin, γ the gyromagnetic ratio of the nuclear isotope (in frequency units) and ∆ν(t) is the time-dependent detuning between the radio frequency (RF) excitation and the Larmor frequency ν L = γB z . The coupling between the RF magnetic field B x and the spin, the second term in the Hamiltonian, leads to an avoided crossing in the eigen-energies with splitting hν RF , Fig. 1a , where ν RF = γB x . On traversing the avoided crossing from large and negative ∆ν to large and positive ∆ν with a single pulse (N = 1) at sweep rate α, the probability that t...

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Manipulation of the nuclear spin ensemble in a quantum dot with chirped magnetic resonance pulses

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“…Interference between two LZ transitions has been observed in gaseous molecules [9], semiconductor-based quantum dots [10], NV centers [11], and atoms in optical lattices [12]. Evidence for various interference effects involving multiple LZ transitions has been observed in the steady-state behavior of continuously driven superconducting qubits [13,14] and NV centers [15].…”

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Observation of Time-Domain Rabi Oscillations in the Landau-Zener Regime with a Single Electronic Spin

et al. 2014

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Under resonant conditions, a long sequence of landau-zener transitions can lead to Rabi oscillations. Using a nitrogen-vacancy (NV) center spin in diamond, we investigated the interference between more than 100 Landau-Zener processes. We observed the new type of Rabi oscillations of the electron spin resulting from the interference between successive Landau-Zener processes in various regimes, including both slow and fast passages. The combination of the control techniques and the favorable coherent properties of NV centers provides an excellent experimental platform to study a variety of quantum dynamical phenomena. The phenomenon of Rabi oscillations, first studied in 1937 [1], occurs in almost any quantum system under the influence of resonant external driving and is at the heart of various spectroscopic techniques. Landau-Zener (LZ) transitions, first studied in 1932 [2][3][4][5], are intriguing phenomena that are ubiquitous in quantum systems, typically occurring when two energy levels of a quantum system undergo an avoided crossing.Under suitable conditions LZ transitions can be treated as quantum coherent processes, and multiple such processes can interfere constructively or destructively [4]. Depending on the details of the interference, a long and regular sequence of LZ processes can exhibit resonance behavior similar to that seen in Rabi oscillations under weak driving conditions.The oscillations obtained in the case of constructive interference can therefore be seen as a manifestation of Rabi oscillations in the regime of ultrastrong driving [6]. Moreover, the interference between LZ processes gives rise to a number of novel features distinct from the case of weak driving. Particularly interesting is the fact that the patterns of the resonance lines vary drastically depending on whether each passage through the avoided crossing is slow or fast [6].The experimental observation of Rabi oscillations in the LZ regime requires stringent conditions. The coherence time of the quantum system is required to be long enough to allow the coherent interference between multiple LZ processes, and the control fields are required to be accurate and stable in order to precisely adjust the quantum phases that govern the interference effects. In addition, the time resolution of the measurement needs to be high enough to allow the monitoring of the dynamics on short timescales.With the recent advances in various quantum systems [7,8], a number of experiments were able to demonstrate the controlled interference of LZ transitions. Interference between two LZ transitions has been observed in gaseous molecules [9], semiconductor-based quantum dots [10], NV centers [11], and atoms in optical lattices [12]. Evidence for various interference effects involving multiple LZ transitions has been observed in the steady-state behavior of continuously driven superconducting qubits [13,14] and NV centers [15]. However, although those steady-state behaviors have been reported, the experimental observation of the abundant time-domain evolu...

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“…Having the purpose of presenting and describing specific results for the multiphoton transitions, our consideration is limited to the Josephson-junction qubits. We note however that similar phenomena can be studied in different quantum objects, which can be described as two-or multi-level systems, such as quantum wires and dots [56][57][58][59][60], nitrogen vacancy centers in diamond [61,62], ultracold atoms [63][64][65], nanomechanical and optomechanical setups [66][67][68], electronic spin systems, two-dimensional electron gas, and graphene [69][70][71].…”

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Multiphoton transitions in Josephson-junction qubits (Review Article)

Shevchenko¹,

Omelyanchouk²,

Il’ichev³

2012

Low Temperature Physics

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Two basic physical models, a two-level system and a harmonic oscillator, are realized on the mesoscopic scale as coupled qubit and resonator. The realistic system includes moreover the electronics for controlling the distance between the qubit energy levels and their populations and to read out the resonator's state, as well as the unavoidable dissipative environment. Such rich system is interesting both for the study of fundamental quantum phenomena on the mesoscopic scale and as a promising system for future electronic devices.We present recent results for the driven superconducting qubit -resonator system, where the resonator can be realized as an LC circuit or a nanomechanical resonator. Most of the results can be described by the semiclassical theory, where a qubit is treated as a quantum two-level system coupled to the classical driving field and the classical resonator. Application of this theory allows to describe many phenomena for the single and two coupled superconducting qubits, among which are the following: the equilibrium-state and weak-driving spectroscopy, Sisyphus damping and amplification, Landau-Zener-Stückelberg interferometry, the multiphoton transitions of both direct and ladder-type character, and creation of the inverse population for lasing. Contents

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Landau-Zener-Stückelberg Interferometry of a Single Electronic Spin in a Noisy Environment

Cited by 64 publications

References 32 publications

Manipulation of the nuclear spin ensemble in a quantum dot with chirped magnetic resonance pulses

Manipulation of the nuclear spin ensemble in a quantum dot with chirped magnetic resonance pulses

Observation of Time-Domain Rabi Oscillations in the Landau-Zener Regime with a Single Electronic Spin

Multiphoton transitions in Josephson-junction qubits (Review Article)

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