Photon-assisted Landau-Zener transition: Role of coherent superposition states

Sun, Zhe; Ma, Jian; Wang, Xiaoguang; Nori, Franco

doi:10.1103/physreva.86.012107

Cited by 38 publications

(46 citation statements)

References 51 publications

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“…40 While much is still unknown about the underlying physics of the dissipative LZSM model, recent attention has been devoted to a superconducting qubit coupled to a single harmonic oscillator of frequency ω. 18,24,[40][41][42][43] For example, a circuit QED device has been experimentally realized by coupling the charge qubit to the superconducting resonator through an electric field. The charge qubit and the resonator have been used to represent the standard LZSM model and the harmonic oscillator, respectively.…”

Section: Introductionmentioning

confidence: 99%

“…Moreover, the off-diagonal qubitoscillator coupling has not been adequately treated if the initial oscillator state is not the vacuum state. [41][42][43] In this work, we will shed some light on the issues mentioned by investigating how an initial number state of the oscillator affects the LZSM dynamics of a two-level system coupled to a single harmonic oscillator using the multi-D 2 -Ansatz with the Dirac-Frenkel variational principle.…”

Section: Introductionmentioning

confidence: 99%

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Davydov-Ansatz for Landau-Zener-Stueckelberg-Majorana transitions in an environment: Tuning the survival probability via number state excitation

Werther

Großmann

Huang

et al. 2019

The Journal of Chemical Physics

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We theoretically investigate transitions in a two-level system, which are induced by a sweep through an avoided crossing in the presence of coupling to a single, excited bosonic mode. This allows us to propose the initial bosonic excitation into a number state as a new possible control parameter for the survival probability at long times. The expansion of number states in terms of coherent states centered around points on a circle in phase space makes a multi-Davydov-Ansatz the method of choice to perform the required numerical calculations. It is revealed that the starting time of the transition greatly affects the final transition probabilities. In addition, we found that the mixing angle, which is tuning between the diagonal and off-diagonal coupling, is decisive for the ability to control the transition via number state excitation. For a mixing angle of π/4, we found the maximal effect of number state excitation on the transition probability.Published under license by AIP Publishing. https://doi. ARTICLEscitation.org/journal/jcp FIG. 7. Transition probabilities as a function of n: θ = 0 (blue), θ = π/4 (red), and θ = π/2 (green). APPENDIX: PROPERTIES OF THE DISPLACEMENT OPERATOR AND THE LAGUERRE POLYNOMIALSIn the following, we collect properties of the displacement operator and its action on number states that are frequently needed in

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Davydov-Ansatz for Landau-Zener-Stueckelberg-Majorana transitions in an environment: Tuning the survival probability via number state excitation

Werther

Großmann

Huang

et al. 2019

The Journal of Chemical Physics

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“…For the case of N = 1 and E c = 0, the resulting model can be used to describe the LZ process in a quantum two-level system coupled to a photon mode [40]. By employing a unitary transformation U = e iωtb † b , the quantum Hamiltonian (23) is equivalent to an effective Hamiltonian…”

Section: Quantization Of the Periodic Driving Fieldmentioning

confidence: 99%

Photon-induced sideband transitions in a many-body Landau-Zener process

et al. 2014

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We investigate the many-body Landau-Zener (LZ) process in a two-site Bose-Hubbard model driven by a time-periodic field. We find that the driving field may induce sideband transitions in addition to the main LZ transitions. These photon-induced sideband transitions are a signature of the photon-assisted tunneling in our many-body LZ process. In the strong interaction regime, we develop an analytical theory for understanding the sideband transitions, which is confirmed by our numerical simulation. Furthermore, we discuss the quantization of the driving field. In the effective model of the quantized driving field, the sideband transitions can be understood as the LZ transitions between states of different "photon" numbers.

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“…The arrow sketches a slow modulation of the bare qubit energy splitting represented by the blue and red lines. The dashed lines are the energies of three harmonic modes.the quantum regime has focused on two-level systems, aside from theoretical considerations [47][48][49][50][51][52][53]. Yet, systems possessing more complicated spectrum, if exposed to LZS conditions, can give new insight in manybody phenomena, or possible applications in quantum control.…”

mentioning

confidence: 99%

“…(3) describe the regular LZS interference problem. One also uses the term photon assisted LZS interference [28,30,51], since the qubit extracts a photon from the excitation field such that its energy is redefined as ω 0 − ω ext .…”

mentioning

confidence: 99%

Landau-Zener-Stückelberg Interference in a Multimode Electromechanical System in the Quantum Regime

et al. 2019

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The studies of mechanical resonators in the quantum regime not only provide insight into the fundamental nature of quantum mechanics of massive objects, but also introduce promising platforms for novel hybrid quantum technologies. Here we demonstrate a configurable interaction between a superconducting qubit and many acoustic modes in the quantum regime. Specifically, we show how consecutive Landau-Zener-Stückelberg (LZS) tunneling type of transitions, which take place when a system is tuned through an avoided crossing of the coupled energy levels, interfere in a multimode system. The work progresses experimental LZS interference to cover situations where the coupled levels are those of a qubit interacting with a multitude of mechanical oscillators in the quantum limit. The work opens up applications in controlling multiple acoustic modes via parametric modulation.Advances in the control over mechanical degrees of freedom have taken great leaps forward allowing to engineer experiments that go deep into the quantum regime, consequently showing the underlying nature of the quantized vibration energy [1][2][3][4][5][6][7]. These works predominantly utilized superconducting quantum bits combined with a variety of different types of mechanical resonators that can be accessed resonantly through the qubit in the high gigahertz frequency range. The resonators can be made with surface acoustic waves (SAW) [5, 7-12], phononic crystals [6], or high overtone bulk acoustic wave resonators (HBAR) [2,13,14], with piezoelectric materials allowing for strong coupling between electric and mechanical quantities. Mechanical modes are better isolated from the electromagnetic environment and can have longer coherence times than superconducting qubits. They are also much more compact than microwave cavities [15,16]. Therefore, incorporating mechanical resonators is highly appealing in quantum computing that can utilize harmonic oscillators [17,18].In an HBAR system, the modes mostly reside in the substrate chip and hence feature diluted strain and low acoustic losses. The system exhibits a dense spectrum of acoustic modes that interact near resonance with the qubit, suggesting a possibility to manipulate the manymode system through the qubit. One way to do the latter is to combine slow adiabatic changes and abrupt rotations of the adiabatic basis. This type of control of qubits resembles a coherent version of Landau-Zener tunneling transitions, which have been studied extensively in various two-level systems either in quantum or classical limit. These include superconducting qubits [19][20][21][22][23][24][25][26][27][28][29][30][31][32], nanomechanical systems [33][34][35][36][37][38], Bose-Einstein condensates [34,39,40], optical lattices [41], and other systems [42][43][44][45][46].In Landau-Zener-Stückelberg (LZS) interference, the system energy levels are modulated back and forth through an avoided crossing at a frequency ω rf faster than the decay rates. Earlier work on LZS physics in |e |g |g, 1 (2)Photon-assisted Landau-Zener-S...

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Photon-assisted Landau-Zener transition: Role of coherent superposition states

Cited by 38 publications

References 51 publications

Davydov-Ansatz for Landau-Zener-Stueckelberg-Majorana transitions in an environment: Tuning the survival probability via number state excitation

Davydov-Ansatz for Landau-Zener-Stueckelberg-Majorana transitions in an environment: Tuning the survival probability via number state excitation

Photon-induced sideband transitions in a many-body Landau-Zener process

Landau-Zener-Stückelberg Interference in a Multimode Electromechanical System in the Quantum Regime

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