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Register a new userUnravelling Quantum Dot Array Simulators via Singlet-Triplet Measurements
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Recently, singlet-triplet measurements in double dots have emerged as a powerful tool in quantum information processing. In parallel, quantum dot arrays are being envisaged as analog quantum simulators of many-body models. Thus motivated, we explore the potential of the above singlet-triplet measurements for probing and exploiting the ground-state of a Heisenberg spin chain in such a quantum simulator. We formulate an efficient protocol to discriminate the achieved many-body ground-state with other likely states. Moreover, the transition between quantum phases, arising from the addition of frustrations in a $J_1-J_2$ model, can be systematically explored using the same set of measurements. We show that the proposed measurements have an application in producing long distance heralded entanglement between well separated quantum dots. Relevant noise sources, such as non-zero temperatures and nuclear spin interactions, are considered.
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We study spin relaxation in a two-electron quantum dot in the vicinity of the singlet-triplet crossing. The spin relaxation occurs due to a combined effect of the spin-orbit, Zeeman, and electron-phonon interactions. The singlet-triplet relaxation rates exhibit strong variations as a function of the singlet-triplet splitting. We show that the Coulomb interaction between the electrons has two competing effects on the singlet-triplet spin relaxation. One effect is to enhance the relative strength of spin-orbit coupling in the quantum dot, resulting in larger spin-orbit splittings and thus in a stronger coupling of spin to charge. The other effect is to make the charge density profiles of the singlet and triplet look similar to each other, thus diminishing the ability of charge environments to discriminate between singlet and triplet states. We thus find essentially different channels of singlet-triplet relaxation for the case of strong and weak Coulomb interaction. Finally, for the linear in momentum Dresselhaus and Rashba spin-orbit interactions, we calculate the singlet-triplet relaxation rates to leading order in the spin-orbit interaction, and find that they are proportional to the second power of the Zeeman energy, in agreement with recent experiments on triplet-to-singlet relaxation in quantum dots.
We present measurements of the capacitive coupling energy and the inter-dot capacitances in a linear quadruple quantum dot array in undoped Si/SiGe. With the device tuned to a regime of strong ($>$1 GHz) intra-double dot tunnel coupling, as is typical for double dot qubits, we measure a capacitive coupling energy of $20.9 pm 0.3$ GHz. In this regime, we demonstrate a fitting procedure to extract all the parameters in the 4D Hamiltonian for two capacitively coupled charge qubits from a 2D slice through the quadruple dot charge stability diagram. We also investigate the tunability of the capacitive coupling energy, using inter-dot barrier gate voltages to tune the inter- and intra-double dot capacitances, and change the capacitive coupling energy of the double dots over a range of 15-32 GHz. We provide a model for the capacitive coupling energy based on the electrostatics of a network of charge nodes joined by capacitors, which shows how the coupling energy should depend on inter-double dot and intra-double dot capacitances in the network, and find that the expected trends agree well with the measurements of coupling energy.
We investigate two serially-aligned quantum dots in the molecular regime of large tunnel couplings t. A Zeeman field B is used to tune the energy difference of singlet and triplet spin configurations. Attaching this geometry to BCS source and drain leads with gap Delta and phase difference phi gives rise to an equilibrium supercurrent J. To compute J in presence of Coulomb interactions U between the dot electrons, we employ the functional renormalization group (FRG). For Bsimt -- where the singlet and lowest-lying triplet spin states are equal in energy -- the current exhibits characteristics of a 0-pi transition similar to a single impurity. Its magnitude in the pi phase, however, jumps discontinuously at B=t, being smaller on the triplet side. Exploiting the flexibility of the FRG, we demonstrate that this effect is generic and calculate J for realistic experimental parameters Delta, U, and gate voltages epsilon. To obtain a more thorough understanding of the discontinuity, we analytically treat the limit Delta=infty where one can access the exact many-particle states. Finally, carrying out perturbation theory in the dot-lead couplings substantiates the intuitive picture that Cooper pair tunneling is favored by a singlet spin configuration while inhibited by a triplet one.
We report individual confinement and two-axis qubit operations of two electron spin qubits in GaAs gate-defined sextuple quantum dot array with integrated micro-magnet. As a first step toward multiple qubit operations, we demonstrate coherent manipulations of three singlet-triplet qubits showing underdamped Larmor and Ramsey oscillations in all double dot sites. We provide an accurate measure of site site-dependent field gradients and rms electric and magnetic noise, and we discuss the adequacy of simple rectangular micro-magnet for practical use in multiple quantum dot arrays. We also discuss current limitations and possible strategies for realizing simultaneous multi multi-qubit operations in extended linear arrays.
We analyze the ground state properties of an array of quantum dots connected in series between superconducting electrodes. This system is represented by a finite Hubbard chain coupled at both ends to BCS superconductors. The ground state is obtained using the Lanczos algorithm within a low energy theory in which the bulk superconductors are replaced by effective local pairing potentials. We study the conditions for the inversion of the sign of the Josephson coupling ($pi$-junction behavior) as a function of the model parameters. Results are presented in the form of phase diagrams which provide a direct overall view of the general trends as the size of the system is increased, exhibiting a strong even-odd effect. The analysis of the spin-spin correlation functions and local charges give further insight into the nature of the ground state and how it is transformed by the presence of superconductivity in the leads. Finally we study the scaling of the Josephson current with the system size and relate these results with previous calculations of Josephson transport through a Luttinger liquid.
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