We study the triangular antiferromagnet Cu3 in external electric fields, using symmetry group arguments and a Hubbard model approach. We identify a spin-electric coupling caused by an interplay between spin exchange, spin-orbit interaction, and the chirality of the underlying spin texture of the molecular magnet. This coupling allows for the electric control of the spin (qubit) states, e.g. by using an STM tip or a microwave cavity. We propose an experimental test for identifying molecular magnets exhibiting spin-electric effects. [5,6,7], or the decoherence and the transition from quantum to classical behavior [8]. SMMs with antiferromagnetic coupling between neighboring spins are especially promising for the encoding and manipulation of quantum information [9,10,11,12], for they act as effective two-level systems, while providing additional auxiliary states that can be exploited for performing quantum gates, even in the presence of untunable couplings between the qubits [13]. Intra-and inter-molecular couplings of SMMs can be engineered by molecular and supra-molecular chemistry [14], enabling a bottom-up design of molecule-based devices [15].While the properties of SMMs can be modfied during the synthesis, control on the time scales required for quantum information processing remains a challenge. The standard spin-control technique is electron spin resonance (ESR) driven by ac magnetic fields B ac (t) [8,16,17,18]. For manipulation on the time scale of 1 ns (Rabi frequency Ω R ∼ 10 9 s −1 ) B ac should be of the order of 10 −2 T, which, however, is difficult to achieve. The spatial resolution of 1 nm, required for addressing a single molecule, is also prohibitively small. At these spatial and temporal scales, the electric control is preferable, because strong electric fields can be applied to small regions by using, for example, STM tips [19,20,21]. Also, the quantized electric field inside a microwave cavity can be used [22,23,24,25] to control single qubits and to induce coupling between them even if they are far apart.Here we identify and study an efficient spin-electric coupling mechanism in SMMs which is based on an interplay of spin exchange, spin-orbit interaction (SOI), and lack of inversion symmetry. Spin-electric effects induced solely by SOI [26] have been proposed [27] and experimentally demonstrated [28] in quantum dots. However, these SOI effects scale with the system size L as L 3 [27], making them irrelevant for the much smaller SMMs. Thus, additional ingredients-such as broken symmetriesmust be present in SMMs for an efficient coupling between spin and applied electric field.In the following, we demonstrate the possibility of such spin-electric effects in SMMs by focusing on a specific example, namely an equilateral spin triangle, Cu 3 [29]. In this SMM, the low energy states exhibit a chiral spin texture and, due to the absence of inversion symmetry, electric fields couple states of opposite chirality. Moreover, SOI couples the chirality to the total spin, and thus an effective spin-electri...
We study a large ensemble of nuclear spins interacting with a single electron spin in a quantum dot under optical excitation and photon detection. At the two-photon resonance between the two electron-spin states, the detection of light scattering from the intermediate exciton state acts as a weak quantum measurement of the effective magnetic (Overhauser) field due to the nuclear spins. In a coherent population trapping state without light scattering, the nuclear state is projected into an eigenstate of the Overhauser field operator, and electron decoherence due to nuclear spins is suppressed: We show that this limit can be approached by adapting the driving frequencies when a photon is detected. We use a Lindblad equation to describe the driven system under photon emission and detection. Numerically, we find an increase of the electron coherence time from 5 to 500 ns after a preparation time of 10 micros.
Molecular nanomagnets show clear signatures of coherent behavior and have a wide variety of effective low-energy spin Hamiltonians suitable for encoding qubits and implementing spin-based quantum information processing. At the nanoscale, the preferred mechanism for control of quantum systems is through application of electric fields, which are strong, can be locally applied, and rapidly switched. In this work, we provide the theoretical tools for the search for single molecule magnets suitable for electric control. By group-theoretical symmetry analysis we find that the spin-electric coupling in triangular molecules is governed by the modification of the exchange interaction, and is possible even in the absence of spin-orbit coupling. In pentagonal molecules the spin-electric coupling can exist only in the presence of spin-orbit interaction. This kind of coupling is allowed for both $s=1/2$ and $s=3/2$ spins at the magnetic centers. Within the Hubbard model, we find a relation between the spin-electric coupling and the properties of the chemical bonds in a molecule, suggesting that the best candidates for strong spin-electric coupling are molecules with nearly degenerate bond orbitals. We also investigate the possible experimental signatures of spin-electric coupling in nuclear magnetic resonance and electron spin resonance spectroscopy, as well as in the thermodynamic measurements of magnetization, electric polarization, and specific heat of the molecules.Comment: 31 pages, 24 figure
We analyze the low-energy spectrum of a two-electron double quantum dot under a potential bias in the presence of an external magnetic field. We focus on the regime of spin blockade, taking into account the spin orbit interaction and hyperfine coupling of electron and nuclear spins. Starting from a model for two interacting electrons in a double dot, we derive a perturbative, effective twolevel Hamiltonian in the vicinity of an avoided crossing between singlet and triplet levels, which are coupled by the spin-orbit and hyperfine interactions. We evaluate the level splitting at the anticrossing, and show that it depends on a variety of parameters including the spin orbit coupling strength, the orientation of the external magnetic field relative to an internal spin-orbit axis, the potential detuning of the dots, and the difference between hyperfine fields in the two dots. We provide a formula for the splitting in terms of the spin orbit length, the hyperfine fields in the two dots, and the double dot parameters such as tunnel coupling and Coulomb energy. This formula should prove useful for extracting spin orbit parameters from transport or charge sensing experiments in such systems. We identify a parameter regime where the spin orbit and hyperfine terms can become of comparable strength, and discuss how this regime might be reached.
We show how to eliminate the first-order effects of the spin-orbit interaction in the performance of a two-qubit quantum gate. Our procedure involves tailoring the time dependence of the coupling between neighboring spins. We derive an effective Hamiltonian which permits a systematic analysis of this tailoring. Time-symmetric pulsing of the coupling automatically eliminates several undesirable terms in this Hamiltonian. Well chosen pulse shapes can produce an effectively isotropic exchange gate, which can be used in universal quantum computation with appropriate coding. PACS: 03.67.Lx, 71.70.Ej, 85.35.Be The exchange interaction between spins is a promising physical resource for constructing two-qubit quantum gates in quantum computers [1][2][3][4][5]. In the idealized case of vanishing spin-orbit coupling, this interaction is isotropic, and any Hamiltonian describing time-dependent exchange between two spin-1/2 qubits, H 0 (t) = J(t)S 1 · S 2 , commutes with itself at different times. Thus, the resulting quantum gate depends on J(t) only through its time integral -a convenient simplification, particularly because, when carrying out quantum gates, the exchange interaction should be pulsed adiabatically on time scales longer thanh/∆E, where ∆E is a typical level spacing associated with the internal degrees of freedom of the qubits [3]. In addition, isotropic exchange alone has been shown to be sufficient for universal quantum computation, provided the logical qubits of the computer are properly encoded [6,7].Given the potential advantages of isotropic exchange for quantum gates, it is important to understand the effect of the inevitable anisotropic corrections due to spinorbit coupling. When these corrections are included, the Hamiltonian describing time-dependent exchange iswhereHere β(t) is the Dzyaloshinski-Moriya vector, which is first order in spin-orbit coupling, and IΓ(t) is a symmetric tensor which is second order in spin-orbit coupling [8]. Although these corrections may be small, they will, in general, not be zero unless forbidden by symmetry. For example, Kavokin has recently estimated that β(t) can be as large as 0.01 for coupled quantum dots in GaAs [9]. In this Letter we construct the quantum gates produced by pulsing H(t). This is nontrivial because H(t) typically does not commute with itself at different times. We represent the resulting gates using an effective Hamiltonian H(t), which we derive perturbatively in powers of the spin-orbit coupling. H(t) is simple to work with because it does commute with itself at different times. As an application of this effective Hamiltonian, we use it to tailor pulse forms that effectively eliminate any firstorder anisotropic corrections.The quantum gate obtained by pulsing a particular H(t) is found by solving the time-dependent Schrödinger equation i d dt |Ψ(t) = H(t)|Ψ(t) where |Ψ(t) is the state vector describing the two spin-1/2 qubits (here, and in what follows,h = 1). In general this problem cannot be solved analytically. However, since we expect spin...
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