Multiqudit interactions in molecular spins

Abstract

We study photon-mediated interactions between molecular spin qudits in the dispersive regime of operation. We derive from a microscopic model the effective interaction between molecular spins, including their crystal field anisotropy (i.e., the presence of nonlinear spin terms) and their multilevel structure. Finally, we calculate the long-time dynamics for a pair of interacting molecular spins using the method of multiple-scale analysis. This allows us to find a set of two-qudit gates that can be realized for a specific choice of molecular spins and to determine the time required for their implementation. Our results are relevant for the implementation of logical gates in general systems of qudits with unequally spaced levels or to determine an adequate computational subspace to encode and process the information.

Molecular nanomagnets: a viable path toward quantum information processing?

“…Therefore, it allows for implementing a generalized iSWAP or √ i SWAP gate between the two qubits at a rate determined by J/h. This result can be generalized to the case of S > 1/2 spin qudits, provided that the dispersive condition applies to all their transition frequencies [288]. The effective spin Hamiltonian (20) becomes then more complex and includes a state dependent coupling tensor.…”

“…The situation is far more challenging in the case of 'real' spins, such as those present in magnetic molecules, which interact with the cavity magnetic field. The generalization of Jaynes-Cumming model (16) to this situation gives [287,288]…”

“…ive regime. The coupling of multiple spins to a single resonator mode can be treated by an extension of equation ( 17) [288]. For illustrative purposes, we consider here the case of two spins S with uniaxial anisotropy and a geometry in which the external magnetic field points along the molecular axes z, while the cavity field is perpendicular to it.…”

Tunable photon-mediated interactions between spin-1 systems

“…Since quantum emitters, like atomic systems, can have a much richer level structure, there is an increasing interest in the last few years [48][49][50][51] on harnessing them to find exotic phenomena, such as multicritical behavior in Dicke phase transitions [48] or emergent dark entangled states [51], as well as to develop * a.gonzalez.tudela@csic.es new applications, such as new multiphoton sources [51]. One very attractive reason for considering multilevel emitters is the possibility to engineer photon-mediated interactions between higher-dimensional spins, which can find applications in the quantum simulation of nontrivial high-energy physics problems [52][53][54][55][56][57], to prepare symmetry-protected topological states in spin-1 chains [58,59], to solve complex optimization problems [60], and, more generally, to engineer universal quantum gates between spin-1 systems [61,62].…”

“…To characterize them, we use projection operator techniques for open quantum systems [63] to find the effective dynamics and characterize the performance of the interactions as entangling gates. We do our analysis in two steps: first, in a platform-agnostic way, so that our results can be of interest to different type of multilevel emitters (such as quantum dots, vacancy centers, molecules [62] or atoms), and then, particularizing for the multilevel structure of a particular atom, i.e., rubidium. In the latter case, we fully take into account the different Clebsch-Gordan coefficients of the transitions and explain how to compensate the corrections introduced by them.…”