Entangling Remote Nuclear Spins Linked by a Chromophore

Abstract

Molecular nanostructures may constitute the fabric of future quantum technologies, if their degrees of freedom can be fully harnessed. Ideally one might use nuclear spins as low-decoherence qubits and optical excitations for fast controllable interactions. Here, we present a method for entangling two nuclear spins through their mutual coupling to a transient optically excited electron spin, and investigate its feasibility through density-functional theory and experiments on a test molecule. From our calculations we identify the specific molecular properties that permit high entangling power gates under simple optical and microwave pulses; synthesis of such molecules is possible with established techniques. DOI: 10.1103/PhysRevLett.104.200501 PACS numbers: 03.67.Bg, 03.67.Lx, 31.15.EÀ, 33.40.+f Molecules are promising building blocks for quantum technologies, due to their reproducible nature and ability to self-assemble into complex structures. However, the need to control interactions between adjacent qubits represents a key challenge [1][2][3][4]. We here describe a method for optical control of a nuclear spin-spin interaction that presents several advantages over conventional NMR quantum processors: the spin-spin interaction can be switched, the gates are faster, and the larger energy transitions facilitate polarization transfer onto the nuclear spins. After explaining the theory behind our method, we present an experimental study of a test molecule, and show with density-functional theory that an entangling gate could be achieved.We consider two nuclear spin qubits labeled n and n 0 and one mediator e. The mediator possesses a paramagnetic excited state jei with spin one character and a diamagnetic, spinless ground state j0i. The two nuclear qubits do not interact with each other directly, but both couple to the excitation via an isotropic hyperfine (HF) coupling with generally unequal strengths A and A 0 , see Fig. 1(a). The Hamiltonian in a magnetic field is given by (@ ¼ 1):where S z;i and S i are the Pauli spin operators and ! i denotes the respective Zeeman splittings (i ¼ n, n 0 , e). D is the zero-field-splitting (ZFS). ! 0 denotes the optical frequency corresponding to the creation energy of the excitation. Let us first analyze the case of a symmetric (homonuclear) system with ! n ¼ ! n 0 and A ¼ A 0 . Using degenerate perturbation theory and assuming that the electronic Zeeman splitting is much larger than that of the nuclei, ! n ( ! e and the ZFS, D ( ! e , we obtain an effective Hamiltonian by approximating H sym : ¼ hejHjei; thus,where V ¼ ðjc 1 ijc 2 i Á Á Á jc 12 iÞ is the matrix of the approximate eigenvectors up to first order and the E i (i ¼ 1; . . . ; 12) are the eigenenergies up to second order. This reveals that the time evolution of the entire system can be

Creating nuclear spin entanglement using an optical degree of freedom

“…[23]. After a short laser pulse for the optical excitation, subspaces T 0,± were found to be populated as p − = 0.49, p 0 = 0.02, and p + = 0.49 with associated lifetimes τ − = 0.57 ms, τ 0 = 0.02 ms, and τ + = 0.57 ms. We assume that the nuclear spins are initialized in state |↓↑ .…”

“…V contains a summary and discussion of our results. Throughout this paper, we closely relate our general ideas to the recent experiments [23,24] which have motivated our analysis, but we would like to point out that our results are more widely applicable and not limited to these specific systems.…”

“…Motivated by recent experimental data from a promising candidate molecule [23], we now analyze the implications of having an initial mixture of the states |T 0 , and |T ± . Experiments on a 13 C-labeled methanocarbon of the diethyl malonate monoadduct (DEMF) reveal that the population of the electronic excitation in a sample oriented along the z axis are equally distributed between |T + and |T − .…”

“…In the second case we use the enhanced protocol described at the end of the section; switching times here are π 4a+ and 3π 4a− . The nuclear spins for both curves are assumed to be initially in state | ↓↑ ; for parameters we use the values found in a recent characterization experiment [23]: D = −296 MHz, ω e = 9.6 GHz, ω n = 3.7 MHz, τ − = 0.57 ms, τ 0 = 0.02 ms, and τ + = 0.57 ms.…”

“…We consider two different initial states for the mediator spin: a completely polarized state and the mixed state reported in Ref. [23].…”