“Stückelberg Interferometry” with Ultracold Molecules

Mark, Manfred J.; Kraemer, T.; Waldburger, P.; Herbig, Jens; Chin, Cheng; Nägerl, Hanns‐Christoph; Grimm, Rudolf

doi:10.1103/physrevlett.99.113201

Cited by 74 publications

(75 citation statements)

References 24 publications

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“…The beam-splitters are tuned by ∆ ptb /Γ c to maximize contrast, the phase measurement reveals the "elevator speed"ε ∝ ∆ ptb Γ c , and the temperature smearing allows absolute calibration of the energy scales. Our scheme is conceptually related to Landau-Zener-Stückelberg interferometry [26][27][28] which measures the relative dynamical phase of discrete states via creation of superposition in sequential non-adiabatic level crossings. In contrast, we propose to access the phase of a single localized state measured against a reference point in the continuum (defined by a sufficiently fast decoupling and a sharp Fermi edge).…”

Section: Figmentioning

confidence: 99%

Quantum Fluctuations and Coherence in High-Precision Single-Electron Capture

Kashcheyevs

Timoshenko

2012

Phys. Rev. Lett.

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The phase of a single quantum state is undefined unless the history of its creation provides a reference point. Thus quantum interference may seem hardly relevant for the design of deterministic single-electron sources which strive to isolate individual charge carriers quickly and completely. We provide a counterexample by analyzing the non-adiabatic separation of a localized quantum state from a Fermi sea due to a closing tunnel barrier. We identify the relevant energy scales and suggest ways to separate the contributions of quantum non-adiabatic excitation and backtunneling to the rare non-capture events. In the optimal regime of balanced decay and non-adiabaticity, our simple electron trap turns into a single-lead Landau-Zener-backtunneling interferometer, revealing the dynamical phase accumulated between the particle capture and leakage. The predicted "quantum beats in backtunneling" may turn the error of a single-electron source into a valuable signal revealing essentially non-adiabatic energy scales of a dynamic quantum dot.PACS numbers: 73.63. Kv, 73.23.Hk, 73.21.La Successful demonstration of electron-on-demand sources based on electrostatic modulation of nanoelectronic circuit elements such as dynamic quantum dots [1][2][3] or mesoscopic capacitors [4,5] has offered a prospect of building an electronic analog of few-photon quantum optics [6] that exploits the particle-wave duality and entanglement of individual elementary excitations in a Fermi sea [7][8][9][10]. This ambitious goal is complemented by a long-standing challenge in quantum metrology [11] to untie the definition of ampere from the mechanical units of SI [12] and implement a current standard based on direct counting of discrete charge carriers. So far the overlap between these research directions [13,14] has been rather limited arguably because metrological applications strive to maximize the particle nature of on-demand excitations.Optimizing the trade-off between speed and accuracy of single-electron isolation [2] does require consideration of quantum error mechanisms such as non-adiabatic excitation [15][16][17] or backtunneling [18][19][20][21]. However, these effects have been hard to differentiate experimentally owing to complexity of non-equilibrium many-particle quantum dynamics [22] and experimental challenges in exercising high-speed control of the electrostatic landscape. The quantum phase of the captured particle has been considered thus far as inconsequential for accuracy and inaccessible for measurement unless the particle is ejected into a separate interferometer [10].In this work, we propose a new type of interferometry to measure and thus control the non-equilibrium energy scales governing the decoupling of a dynamic quantum dot from a Fermi sea. Remarkably, our approach requires neither multiple spatial paths [9,10] nor noise measurements [8,22,23], relying instead on quantum beats in spontaneous emission of electrons back to the source lead. Using a generic [22,24] effective single-particle model we predict an interfer...

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Section: Figmentioning

confidence: 99%

Quantum Fluctuations and Coherence in High-Precision Single-Electron Capture

Kashcheyevs

Timoshenko

2012

Phys. Rev. Lett.

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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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confidence: 99%

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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“…Due to the simple form of the Hamiltonian, the LZ model is experimentally obtainable and the transition has been observed in many quantum systems, from Rydeberg atoms [30,31] to quantum dots contacts [32], and recently extended to mesoscopic superconducting Josephson devices [33], ultracold molecules [34], optical lattices [35] and the NV center [36]. There are no technological challenges in controlling the level structure in LZ dynamics in most of these systems and more complicated dynamics based on the LZ model have been presented (see [37] for a review).…”

Section: Methodsmentioning

confidence: 99%

Quantum Simulation of Landau-Zener Model Dynamics Supporting the Kibble-Zurek Mechanism

Han

Sun

et al. 2014

Phys. Rev. Lett.

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The Kibble-Zurek mechanism (KZM) captures the key physics in the non-equilibrium dynamics of second-order phase transitions, and accurately predict the density of the topological defects formed in this process. However, despite much effort, the veracity of the central prediction of KZM, i.e., the scaling of the density production and the transit rate, is still an open question. Here, we performed an experiment, based on a nine-stage optical interferometer with an overall fidelity up to 0.975±0.008, that directly supports the central prediction of KZM in quantum non-equilibrium dynamics. In addition, our work has significantly upgraded the number of stages of the optical interferometer to nine with a high fidelity, this technique can also help to push forward the linear optical quantum simulation and computation.In the early universe after the "Big Bang", cosmological phase transitions occurred with the expansion and cooling of the universe, and the symmetry of the vacuum was broken. The new vacuums were chosen locally, within space-like regions, resulting in topological defects [1,2]. The initial density of the topological defect is extremely interesting, and a rough limit of this density can be estimated by the light-cone causality; however, the exact density is not easy to determine. Zurek suggested that this cosmological mechanism can be observed in condensed matter systems in a laboratory [3][4][5]. For example, a pressure quench drives liquid 4 He from a normal phase to a superfluid phase at a finite rate, which leaves behind vortex lines.In a condensed matter system, the speed limit of the light is less useful to estimate the density of defects. However, the density of topological defects can be predicted for second order phase transitions due to the divergence of the relaxation time τ (which characterizes the time required for the order parameter to relax to its equilibrium value when the parameter has been perturbed) and the healing length (which characterizes the length over which the order parameter will return to the equilibrium value when disturbed) near the critical point. As a result of the divergence, every such transition, traversed at a finite rate, is inevitably a non-equilibrium dynamical process. The whole system can not catch up, and the symmetry will be broken with some topological defects [3][4][5]. Therefore, the Kibble-Zurek mechanism (KZM) provides a theoretical framework with which to describe the non-equilibrium dynamics of the symmetry broken in the second order transition [1][2][3][4][5].The central prediction of the KZM is that the density of the topological defects in the second order phase transition should scale with the transit rate [3][4][5]. To be more specific, consider the phase transition in liquid * smhan@ustc.edu.cn † cfli@ustc.edu.cn 4 He driven by the pressure (denoted here by t) and suppose that the critical point is located at t = 0. The entire dynamic process can be divided into three parts, the adiabatic, impulse and adiabatic regions(which are shown in Fig.1(a)), ...

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“Stückelberg Interferometry” with Ultracold Molecules

Cited by 74 publications

References 24 publications

Quantum Fluctuations and Coherence in High-Precision Single-Electron Capture

Quantum Fluctuations and Coherence in High-Precision Single-Electron Capture

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

Quantum Simulation of Landau-Zener Model Dynamics Supporting the Kibble-Zurek Mechanism

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