Open quantum system description of singlet-triplet qubits in quantum dots
L. K. Castelano, F. F. Fanchini, K. Berrada
备注：
This version provides a description of the decoherence mechanism that is completely different from the published version. For a closer version see arXiv: 1701.03169
We develop a theoretical model to describe the dissipative dynamics of singlet-triplet (S-T_0) qubits in GaAs quantum dots. Using the concurrence experimentally obtained as a guide, we show that each logical qubit is coupled to its own environment because the decoherence effect can be described by independent dephasing channels. Given the correct description of the environment, we study the dynamics of concurrence as a function of the temperature, the constant coupling between the system and the environment, the preparation time, and the exchange coupling. Although the reduction of the environment coupling constant modifies the entanglement dynamics, we demonstrate that temperature emerges as a crucial variable and a variation of millikelvins significantly modifies the generation of entangled states. Furthermore, we show that the exchange coupling together with the preparation time strongly affects the entanglement dissipative dynamics.
Coupled pairs of nuclear spins-1/2 support one singlet state and three triplet states. Transitions between the singlet state and one of the triplet states may be driven by an oscillating low-frequency magnetic field, in the presence of couplings to a third nuclear spin, and a weak bias magnetic field.This phenomenon allows the generation of strong nuclear hyperpolarization of ${}^{13}\mathrm{C}$ nuclei, starting from the nuclear singlet polarization of a ${}^{1}\mathrm{H}$ spin pair, associated with the enriched para spin isomer of hydrogen gas. Hyperpolarization is demonstrated for two molecu…
We propose a resonator-assisted entangling gate for spin qubits with high fidelity. Each spin qubit corresponds to two electrons in a nanowire double quantum dot, with the singlet and one of the triplets as the logical qubit states. The gate is effected by virtual charge dipole transitions. We include noise in our model to show feasibility of the scheme under current experimental conditions.
Coupled pairs of spin-1/2 nuclei support one singlet state and three triplet states. In many circumstances the nuclear singlet order, defined as the difference between the singlet population and the mean of the triplet populations, is a long-lived state which persists for a relatively long time in solution. Various methods have been proposed for generating singlet order, starting from nuclear magnetization. This requires the stimulation of singlet-to-triplet transitions by modulated radiofrequency fields. We show that a recently described pulse sequence, known as PulsePol (Schwartz $\textit{et…
Geometric gates that use the global property of the geometric phase is believed to be a powerful tool to realize fault-tolerant quantum computation. However, for singlet-triplet qubits in semiconductor quantum dot, the low Rabi frequency of the microwave control leads to overly long gating time, and thus the constructing geometric gate suffers more from the decoherence effect. Here we investigate the key issue of whether the fast geometric gate can be realized for singlet-triplet qubits without introducing an extra microwave-driven pulse, while maintaining the high-fidelity gate operation at t…
We develop a theoretical model to describe the dissipative dynamics of singlet-triplet qubits in GaAs quantum dots. Using the concurrence experimentally obtained [M. D. Shulman et al., Science 336, 202 (2012)] as a guide, we found that each logical qubit fluctuates under the action of a random telegraph noise (RTN) that simulates the $1/f^α$ noise. We also study the dynamics of concurrence as a function of the amplitude of the RTN, the correlation time of the RTN, the preparation time of states, and the two-qubit coupling. Furthermore, we show that the two-qubit coupling together with the prep…
The search of a sweet spot, locus in qubit parameters where quantum control is first-order insensitive to noises, is key to achieve high-fidelity quantum gates. Efforts to search for such a sweet spot in conventional double-quantum-dot singlet-triplet qubits where each dot hosts one electron ("two-electron singlet-triplet qubit"), especially for two-qubit operations, have been unsuccessful. Here we consider singlet-triplet qubits allowing each dot to host more than one electron, with a total of four electrons in the double quantum dots ("four-electron singlet-triplet qubit"). We theoretically …
Singlet fission is commonly defined to involve a process by which an overall singlet state with local triplet structure spin-decoheres into two triplet states, thereby completing the fission process. This process, often defined in loose terms involving the multiplicity of the overall state, is investigated here using a uniform Heisenberg spin-chain subject to a dephasing environmental interaction. We introduce new results from quantum information theory which enables the quantification of coherence and entanglement in a bi- and multipartite system. The calculated measures of these quantum effe…
We study a pair of capacitively coupled singlet-triplet spin qubits. We characterize the two-qubit decoherence through two complementary measures, the decay time of coupled-qubit oscillations and the fidelity of entangled state preparation. We provide a quantitative map of their dependence on charge noise and field noise, and we highlight the magnetic field gradient across each singlet-triplet qubit as an effective tool to suppress decoherence due to charge noise.
Singlet-triplet states in double quantum dots are promising realizations of qubits, and capacitive coupling can be used to create entanglement between these qubits. We propose an entangling three-qubit gate of singlet-triplet qubits in a triangular setup. Our simulations using a realistic microscopic model show that a maximally entangled Greenberger-Horne-Zeilinger state can be generated as the qubits are evolved under exchange. Furthermore, our analysis for the gate operation can be used to extract the actual experimental pulse sequence needed to realize this.
We measure singlet-triplet mixing in a precision fabricated double donor dot comprising of 2 and 1 phosphorus atoms separated by $16{\pm}1$ nm. We identify singlet and triplet-minus states by performing sequential independent spin readout of the two electron system and probe its dependence on magnetic field strength. The relaxation of singlet and triplet states are measured to be $12.4{\pm}1.0$ s and $22.1{\pm}1.0$ s respectively at $B_z{=}2.5$ T.
In the singlet-triplet qubit architecture, the two-qubit interactions required in universal quantum computing can be implemented by capacitative coupling, by exploiting the charge distribution differences of the singlet and triplet states. The efficiency of this scheme is limited by decoherence, that can be mitigated by stronger coupling between the qubits. In this paper, we study the capacitative coupling of singlet-triplet qubits in different geometries of the two-qubit system. The effects of the qubit-qubit distance and the relative orientation of the qubits on the capacitative coupling str…
Using single-shot charge detection in a GaAs double quantum dot, we investigate spin relaxation time T_1 and readout visibility of a two-electron singlet-triplet qubit following single-electron dynamic nuclear polarization (DNP). For magnetic fields up to 2 T, the DNP cycle is in all cases found to increase Overhauser field gradients, which in turn decrease T_1 and consequently reduce readout visibility. This effect was previously attributed to a suppression of singlet-triplet dephasing under a similar DNP cycle. A model describing relaxation after singlet-triplet mixing agrees well with exper…
We propose a process to convert ultracold metastable Cs$_2$ molecules in their lowest triplet state into (singlet) ground state molecules in their lowest vibrational levels. Molecules are first pumped into an excited triplet state, and the triplet-singlet conversion is facilitated by a two-step spontaneous decay through the coupled $A^{1}Σ_{u}^{+} \sim b ^{3}Π_{u}$ states. Using spectroscopic data and accurate quantum chemistry calculations for Cs$_2$ potential curves and transition dipole moments, we show that this process has a high rate and competes favorably with the single-photon decay ba…
We present a highly flexible computational scheme for studying correlated electrons confined by an arbitrary external potential in two-dimensional semiconductor quantum dots. The method starts by a Lagrange mesh calculation for the single-particle states, followed by the calculation of the Coulomb interaction matrix elements between these, and combining both in the exact diagonalization of the many-body Hamiltonian. We apply the method in simulation of double quantum dot singlet-triplet qubits. We simulate the full quantum control and dynamics of one singlet-triplet qubit. We also use our meth…
We experimentally demonstrate coherence recovery of singlet-triplet superpositions by interlacing qubit rotations between Carr-Purcell (CP) echo sequences. We then compare performance of Hahn, CP, concatenated dynamical decoupling (CDD) and Uhrig dynamical decoupling (UDD) for singlet recovery. In the present case, where gate noise and drift combined with spatially varying hyperfine coupling contribute significantly to dephasing, and pulses have limited bandwidth, CP and CDD yield comparable results, with T2 ~ 80 microseconds.
Charge noise is the main hurdle preventing high-fidelity operation, in particular that of two-qubit gates, of semiconductor-quantum-dot-based spin qubits. While certain sweet spots where charge noise is substantially suppressed have been demonstrated in several types of spin qubits, the existence of one for coupled singlet-triplet qubits is unclear. We theoretically demonstrate, using full configuration-interaction calculations, that a range of nearly sweet spots appear in the coupled singlet-triplet qubit system when a strong enough magnetic field is applied externally. We further demonstrate…
The $s_z=0$ spin configuration of two electrons confined at a double quantum dot (DQD) encodes the singlet-triplet qubit (STQ). We introduce the inverted STQ (ISTQ) that emerges from the setup of two quantum dots (QDs) differing significantly in size and out-of-plane magnetic fields. The strongly confined QD has a two-electron singlet ground state, but the weakly confined QD has a two-electron triplet ground state in the $s_z=0$ subspace. Spin-orbit interactions act nontrivially on the $s_z=0$ subspace and provide universal control of the ISTQ together with electrostatic manipulations of the c…
In this work we perform direct single-shot readout of the singlet-triplet states in exchange coupled electrons confined to precision placed donor atoms in silicon. Our method takes advantage of the large energy splitting given by the Pauli-spin blockaded (2,0) triplet states, from which we can achieve a single-shot readout fidelity of 98.4$\pm$0.2%. We measure the triplet-minus relaxation time to be of the order 3s at 2.5T and observe its predicted decrease as a function of magnetic field, reaching 0.5s at 1T.
There has been significant progress in the implementation and manipulation of singlet-triplet qubits in GaAs quantum dots. Given the considerably longer spin coherence times measured in Si, considerable interest has been generated recently in Si quantum dots. The physics of these systems is considerably more complex than the physics of GaAs quantum dots owing to the presence of the valley degree of freedom, which constitutes the focus of this work. In this paper we investigate the physics of Si quantum dots and focus on the feasibility of quantum coherent singlet-triplet qubit experiments anal…
We show that singlet-triplet superpositions of two-electron spin states in a double quantum dot undergo a phonon-induced pure dephasing which relies only on the tunnel coupling between the dots and on the Pauli exclusion principle. As such, this dephasing process is independent of spin-orbit coupling or hyperfine interactions. The physical mechanism behind the dephasing is elastic phonon scattering, which persists to much lower temperatures than real phonon-induced transitions. Quantitative calculations performed for a lateral GaAs/AlGaAs gate-defined double quantum dot yield micro-second deph…
The valley degree of freedom in the electronic band structure of silicon, graphene, and other materials is often considered to be an obstacle for quantum computing (QC) based on electron spins in quantum dots. Here we show that control over the valley state opens new possibilities for quantum information processing. Combining qubits encoded in the singlet-triplet subspace of spin and valley states allows for universal QC using a universal two-qubit gate directly provided by the exchange interaction. We show how spin and valley qubits can be separated in order to allow for single-qubit rotation…
We study controllable exchange coupling between two singlet-triplet qubits. We start from the original second quantized Hamiltonian of a quadruple quantum dot system and obtain the effective spin-spin interaction between the two qubits using the projection operator method. Under a strong uniform external magnetic field and an inhomogeneous local micro-magnetic field, the effective interqubit coupling is of the Ising type, and the coupling strength can be expressed in terms of quantum dot parameters. Finally, we discuss how to generate various two-qubit operations using this controllable coupli…
Radical-ion pairs, fundamental for understanding photosynthesis and the avian magnetic compass, were recently shown to be biological open quantum systems. We here show that the coupling of the radical-pair's spin degrees of freedom to its decohering vibrational reservoir leads to a shift of the radical-pair's magnetic energy levels. The Lamb shift Hamiltonian is diagonal in the singlet-triplet basis, and results in a singlet-triplet energy splitting physically indistinguishable from an exchange interaction. This could have significant implications for understanding the energy level structure a…
Radical-pair reactions pertinent to biological magnetic field sensing are an ideal system for demonstrating the paradigm of quantum biology, the exploration of quantum coherene effects in complex biological systems. We here provide yet another fundamental connection between this biochemical spin system and quantum information science. We introduce and explore a formal measure quantifying singlet-triplet coherence of radical-pairs using the concept of quantum relative entropy. The ability to quantify singlet-triplet coherence opens up a number of possibilities in the study of magnetic sensing w…
The exchange interaction in a singlet-triplet qubit defined by two-electron states in the double-quantum-dot system ("two-electron singlet-triplet qubit") typically varies monotonically with the exchange interaction and thus carries no sweet spot. Here we study a singlet-triplet qubit defined by four-electron states in the double-quantum-dot system ("four-electron singlet-triplet qubit"). We demonstrate, using configuration-interaction calculations, that in the four-electron singlet-triplet qubit the exchange energy as a function of detuning can be non-monotonic, suggesting existence of sweet …
The valley degree of freedom presents challenges and opportunities for silicon spin qubits. An important consideration for singlet-triplet states is the presence of two distinct triplets, comprised of valley vs. orbital excitations. Here we show that both of these triplets are present in the typical operating regime, but that only the valley-excited triplet offers intrinsic protection against charge noise. We further show that this protection arises naturally in dots with stronger confinement. These results reveal an inherent advantage for silicon-based multi-electron qubits.
Probing extended polyene systems with energy in excess of the bright state ($1^1B_u^+$/$S_2$) band edge generates triplets via singlet fission. This process is not thought to involve the $2^1A_g^-$/$S_1$ state, suggesting that other states play a role. Using density matrix renormalisation group (DMRG) calculations of the Pariser-Parr-Pople-Peierls Hamiltonian, we investigate candidate states that could be involved in singlet fission. We find that the relaxed $1^1B_u^-$, and $3^1A_g^-$ singlet states and $1^5A_g^-$ quintet state lie below the $S_2$ state. The $1^1B_u^-$, $3^1A_g^-$ and $1^5A_g^…
We theoretically study the influence of charge noise on a controlled phase gate, implemented using two proximal double quantum dots coupled electrostatically. Using the configuration interaction method, we present a full description of the conditional control scheme and quantitatively calculate the gate error arising from charge fluctuations. Our key finding is that the existence of noise-immune sweet spots depends on not only the energy detuning but also the device geometry. The conditions for sweet spots with minimal charge noise are predicted analytically and verified numerically. Going bey…
We demonstrate the conversion of cold Cs_{2} molecules initially distributed over several vibrational levels of the lowest triplet state a^{3}Σ_{u}^{+} into the singlet ground state X^{1}Σ_{g}^{+}. This conversion is realized by a broadband laser exciting the molecules to a well-chosen state from which they may decay to the singlet state throug\textcolor{black}{h two sequential single-photon emission steps: Th}e first photon populates levels with mixed triplet-singlet character, making possible a second spontaneous emission down to several vibrational levels of the X^{1}Σ_{g}^{+} states. By ad…
Employing a spin-parameterized Kleldysh-Usadel technique for the diffusive regime, we demonstrate that even in the low proximity limit, considerable long-ranged triplet supercurrents can be effectively generated by spin-singlet supercurrents flowing \textit{parallel} to the interfaces of uniform double ferromagnet interlayers with noncollinear exchange fields "{\it independent}" of actual junction geometry. The triplet supercurrents are found to be most pronounced when the thicknesses of the ferromagnet strips are unequal. To experimentally verify this generic phenomenon, we propose an accessi…
