Nonequilibrium Landau-Zener-Stueckelberg spectroscopy in a double quantum dot

Abstract

We study theoretically nonequilibrium Landau-Zener-Stückelberg (LZS) dynamics in a driven double quantum dot (DQD) including dephasing and, importantly, energy relaxation due to environmental fluctuations. We derive effective nonequilibrium Bloch equations. These allow us to identify clear signatures for LZS oscilations observed but not recognized as such in experiments [Petersson et al., Phys. Rev. Lett. 105, 246804, 2010] and to identify the full environmental fluctuation spectra acting on a DQD given experimental data as in [Petersson et al., Phys. Rev. Lett. 105, 246804, 2010]. Herein we find that super-Ohmic fluctuations, typically due to phonons, are the main relaxation channel for a detuned DQD whereas Ohmic fluctuations dominate at zero detuning.PACS numbers: 03.65. Yz,85.35.Gv,73.21.La Quantum electronic devices, as qubits realized by double quantum dots (DQD), require coherence times which exceed their quantum operation time during which the DQD is typically strongly driven by external voltage pulses. Tremendous research efforts studied semiconductor based devices to achieve coherent quantum control [1][2][3][4][5][6][7]. Many fluctuation sources of the noisy solid state environment, which act on the electron in the DQD and thus destroy coherence, were revealed but a comphrehensive picture is elusive. Furthermore, driving by voltage pulses causes an intrinsic nonequilibrium situation in which relaxation competes with driving [8-10] which renders a theoretical description of the dissipative nonequilibrium dynamics highly nontrivial.Here, we theoretically study the dissipative nonequilibrium dynamics of a single electron charge qubit defined in a DQD embedded in a noisy solid state environment driven by voltage pulses. While DQD charge qubits have relatively short coherence times, this disadvantage is compensated by the possibility of fast quantum operations. We model the DQD and its dissipation as a quantum two-level system in an open quantum system approach [11]. We determine the dissipative nonequilibrium real time dynamics (initialized by applying voltage pulses) by deriving effective nonequilibrium Bloch equations (NBEs). These allow fast numerical treatment in contrast to numerical exact methods [8,9] and thus allow a comphrehensive analysis of recent experiments by Petersson et al. [1] and Dovzhenko et al. [12]. In these experiments quantum control of a single electron was achieved by means of applying ultra short voltage pulses to control gates of the laterally defined DQD. In these time ensemble measurements the DQD was cycled (with 40 MHz repetition rate) between two different ground state configurations while its average charge occupation was continuously detected via the electric current through a capacitively coupled quantum point contact (QPC). The applied voltage pulses generate Landau-Zener-Stückelberg (LZS) dynamics [13] and we can identify so far unexplained features in the experimental data as signatures of coherent LZS oscillations.In the experimental ensemble measurements the de...

Ultrafast universal quantum control of a quantum-dot charge qubit using Landau–Zener–Stückelberg interference

“…LZS has also gained particular interest for quantum control814 because it is less sensitive to certain types of noise and might enable the implementation of a universal gate with high fidelity151617. Here we experimentally demonstrate such a scheme for a single-charge qubit in a double quantum dot (DQD), using a single pulse.…”

Dynamic transition in Landau-Zener-Stückelberg interferometry of dissipative systems: The case of the flux qubit

“…The accumulated phase between these repeated tunneling events gives place to constructive or destructive interferences, depending on the driving amplitude and the detuning from the avoided crossing. These LZS interferences have been observed in a variety of quantum systems, such as Rydberg atoms, 2 superconducting qubits, [3][4][5][6][7][8][9][10][11][12][13][14][15] ultracold molecular gases, 16 quantum dot devices, [17][18][19][20][21][22][23][24][25] single spins in nitrogen vacancy centers in diamond, 26,27 nanomechanical circuits, 28 and ultracold atoms in accelerated optical lattices. 29 Several other related experimental and theoretical works have studied LZS interferometry in systems under different shapes of periodic driving, [30][31][32][33][34][35] in two coupled qubits, 36 in optomechanical systems, 37 and the effect of a geometric phase.…”

Characterization of Qubit Dephasing by Landau-Zener-Stückelberg-Majorana Interferometry

“…The probability to remain in the initial qubit state, P LZ = exp(−π∆ 2 /2 v), thereby grows with the velocity v = d /dt, here assumed to be constant [1][2][3][4]. Because the relative phase between the split wavepackets depends on their energy evolutions, repeated passages by a periodic modulation (t) =¯ +A cos(Ωt), give rise to so-called LZSM quantum interference [2][3][4][5][6][7][8][9][10][11][12][13][14][15]. We present a breakthrough which * These authors contributed equally to this work.…”