Hamiltonian engineering of general two-body spin-1/2 interactions

Abstract

Spin Hamiltonian engineering in solid-state systems plays a key role in a variety of applications ranging from quantum information processing and quantum simulations to novel studies of manybody physics. By analyzing the irreducible form of a general two-body spin-1/2 Hamiltonian, we identify all interchangeable interaction terms using rotation pulses. Based on this, we derive novel pulse sequences, defined by an icosahedral symmetry group, providing the most general achievable manipulation of interaction terms. We demonstrate that, compared to conventional Clifford rotations, these sequences offer advantages for creating Zeeman terms essential for magnetic sensing, and could be utilized to generate new interaction forms. The exact series of pulses required to generate desired interaction terms can be determined from a linear programming algorithm. For realizing the sequences, we propose two experimental approaches, involving pulse product decomposition, and off-resonant driving. Resulting engineered Hamiltonians could contribute to the understanding of many-body physics, and result in the creation of novel quantum simulators and the generation of highly-entangled states, thereby opening avenues in quantum sensing and information processing. For many decades, rotation pulse sequences have been utilized in nuclear magnetic resonance (NMR) for manipulating spin states through Hamiltonian engineering [2,3]. In recent years, solid-state spin systems such as defects in diamonds, silicon, and silicon carbide have emerged as useful platforms for quantum technologies, thereby reviving the neccesity in efficient spin control schemes. In particular, the Nitrogen-Vacancy (NV) centers in diamond, which offer optical initialization and readout capabilities, and can be treated to some extent as spin-1/2 qubits, are widely used for sensing [4][5][6][7][8][9][10] and quantum information processing [11][12][13][14]. Manipulating the dipolar interactions within an ensemble of such spins could pave the way towards novel studies of manybody dynamics [15][16][17], the creation of quantum simulators and sensors [18], and generation of non-classical spin states [17,19]. Recent studies of such Hamiltonian engineering, analyzing the effects of control pulses from the Clifford rotation group, resulted in a novel scheme of generating certain types of Hamiltonians [18].Here, we use group theory to go beyond previous work, introducing a more general platform of interaction manipulations, namely pulse sequences defined by an icosahedral symmetry. We emphasize that such pulses can provide the most general achievable manipulations of interaction terms. In particular, by utilizing a linear programming algorithm, we derive the proper sequences for transforming the natural NV-NV dipolar interaction Hamiltonian to several target Hamiltonians providing novel applications, which could not be generated using conventional Clifford rotations.We begin by introducing the general interaction Hamiltonian of N spin-1/2 particles, which contains up to two-bod...

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