Size of linear superpositions in molecular nanomagnets

Abstract

Molecular nanomagnets are zero-dimensional spin systems, that exhibit quantum mechanical behavior at low temperatures. Exploiting quantum-information theoretic measures, we quantify here the size of linear superpositions that can be generated within the ground multiplet of high-and low-spin nanomagnets. Amongst the former class of systems, we mainly focus on Mn12 and Fe8. General criteria for further increasing such sizes are also outlined, and illustrated in the case of spin rings. The actual character (micro or macroscopic) of linear superpositions in low-spin systems is inherently ill-defined. Here, this issue is addressed with specific reference to the Cr7Ni and V15 molecules, characterized by an S = 1/2 ground state. In both cases, the measures we obtain are larger than those of a single s = 1/2 spin, but not proportionate to the number and value of the constituent spins. Molecular nanomagnets represent prototypical examples of engineerable quantum systems. In fact, their physical properties can be widely tuned by chemical synthesis, and quantum coherence effects show up in their spin dynamics [1,2]. These effects include quantum tunneling of the molecule spin, resulting in a speed-up of the magnetization relaxation [3,4], and quantum phase interference [5]. Besides, microwave-induced quantum coherences [6,7] and Rabi oscillations [8,9] were recently observed in a wide class of spin clusters. These experimental achievements, along with the microscopic understanding and chemical control of the decoherence processes [10,11], will possibly enable the use of molecular nanomagnets for quantum-information processing [12,13].Amongst molecular nanomagnets with dominant exchange interaction, a prominent distinction is that between high-and low-spin systems.In the former class of spin clusters, the ground S multiplet may include classical-like states that are macroscopically different from one another, and whose linear superpositions can thus be regarded as Schrödinger cat states [14]. In the latter systems, antiferromagnetic interactions result instead in ground states with low S and highly non-classical features, such as quantum entanglement [15] or Néel-vector tunneling [16][17][18]. Hereafter, we theoretically investigate the size of linear superpositions that can be -or have already beengenerated in both these kinds of molecular nanomagnets. In the case of high-spin molecules, we quantify the actual macroscopicity of linear superpositions. In other words, we determine to which extent their sizes are proportionate to the number and value of the constituent spins, and thus approach the theoretical maxima. We initially focus on the most celebrated single-molecule magnets, [ [20]. In both these nanomagnets (hereafter referred to as Mn 12 and Fe 8 ) the ground state is characterized by a ferrimagnetic ordering, with the total spin S resulting from the inequivalence of the two sublattices [1]. The role played by such inequivalence is further discussed in reference to a prototypical class of spin rings, which includes...

Quantum metrology in Lipkin-Meshkov-Glick critical systems

“…In particular this behavior has been tested in models where the interaction is restricted to first neighbors [9,10,14], e.g., quantum Ising and X-Y models in an external field, in order to precisely estimate the parameters of the system and to provide useful information about the phase diagram. In view of the attention paid to systems with more sophisticated interaction among lattice sites [15][16][17][18] a question thus naturally arises as to whether criticality may be exploited to enhance metrology in systems with interaction beyond the first-neighbor approximation. * matteo.paris@fisica.unimi.it In this framework, systems described by the Lipkin-Meshkov-Glick (LMG) model provide nontrivial examples to assess quantum criticality as a resource for quantum estimation.…”

Thermal transistor effect in quantum systems

“…In parallel, molecular nanomagnets [45] are also attracting more interest as a feasible platform for quantum technological purposes [52]. Specifically, molecular nanomagnets, composed by N = 3 main units, have been proved to be useful for quantum thermometry [53] and for coherent-manipulation of three-qubit states [54].…”

On the Use of Classical and Quantum Fisher Information in Molecular Magnetism

“…The QFI H thus represents a general theoretical tool which allows one to compare the size of different cat-like quantum states prepared in a given molecular nanomagnet (see below), and also in different molecules [23].…”

“…If applied to low-spin molecules with highly-entangled ground states, the calculation of the relative Fisher information leads to the conclusion that linear superpositions of their ground states are in fact rather poor examples of Schrödinger cat states. Broadly speaking, these are systems with highly nonclassical ground states, but the degree of nonclassicality-as quantified by the quantum fluctuations of X-is not significantly enhanced by linearly superimposing the ground states [23]. As a final remark, we would like to mention a possible connection between the QFI of a linear superposition of two eigenstates, |ψ 1 and |ψ 2 , and the transitions |ψ 1 −→ |ψ 2 induced by electron paramagnetic resonance (EPR).…”