Rabi Oscillations in Anisotropic Spins

We are developing an electron spin echo experimental setup operating at 10-30 GHz and ~100 mK. For this, microstrip resonators specifically designed for high sensitivity and homogeneity of the magnetic field at the sample position are being be employed. In order to eliminate dipolar dephasing via polarization of the spin bath one needs to decrease the temperature of the system such that all molecular spins remain in their ground state, avoiding population of excited states and hence eliminating spin fluctuations. Consequently, the temperature required directly depends on the spacing between the ground and first excited states. For example, in experiments designed to study decoherence in Fe₈ performed at the NHMFL, the high microwave frequencies used (>125 GHz) allow spin polarization (i.e., negligible population of the first excited state) for temperatures above 1 K. Unfortunately, a large magnetic field (>10 T) must be employed to sufficiently separate the spin energy states, making the Zeeman coupling the primary energy and the applied field the quantization axis of the system, against the intrinsic molecular anisotropy. This reduces the mixing of spin states which, together with the EPR spin transition selection rules, has made the observation of spin-echo virtually impossible for most SMMs placed in the high-field/high-frequency setup at the NHMFL, regardless of the ability to polarize the spin bath. In addition, phonon excitations become an increasingly dominant source of decoherence at high temperatures. The proposed studies at low temperatures and low magnetic fields that will be enabled by the experimental setup in our group will allow measurements of decoherence rates two orders of magnitude smaller than those attained previously by other groups. The range of energies that the system is designed to sample will also allow for the investigation of the three main sources of decoherence in a single experiment (i.e., dipolar, nuclear and phonon dephasing).

The low microwave energies achievable in this experiment (10-30 GHz) will enable studies of a variety of SMMs without decimating the role of the intrinsic molecular anisotropy by the application of large magnetic fields [the figure above shows a mononuclear (left) and a polynuclear (right) SMM and their respective anisotropy barriers]. This is particularly important for Rabi oscillations induced by pulsed electromagnetic radiation. When a large magnetic field imposes the quantization axis (Zeeman energy), induced transitions occur between spin levels that are eigenstates of the Hamiltonian. In this case, the spin quantum dynamics can be calculated analytically and correspond to simple Rabi oscillations where the system alternates between the two states involved. However, when the anisotropy barrier is comparable to the Zeeman energy, Rabi transitions may involve states resulting from symmetric and antisymmetric superpositions of eigenstates of the Hamiltonian. In this case, the Rabi oscillations are not well defined and the quantum nature of the commutation between the spin operators leads to complex dynamics where the magnetic state of the molecule may develop excited precessional states. This exciting characteristic of the light-matter interaction in magnetic systems is unique for SMMs.

Recent Publications on this topic:

R. Cebulka, and E. del Barco
“Sub-Kelvin (100mK) Time Resolved EPR Spectroscopy for Studies of Quantum Dynamics of Low-Dimensional Spin Systems at Low Frequencies and Magnetic Fields”
Rev. Sci. Instrum. 90, 085106 (2019)

Collaborators:

Physics:
Philip Stamp and Igor Tupitsyn (UBC, Vancouver, Canada)
Seiji Miyashita (UT, Tokio, Japan)

Chemistry:
Eugenio Coronado (UV, Valencia, Spain)
Guillem Aromi (UB, Barcelona, Spain)
Selvan Demir (Michigan, US)