Quantum Coherence and Dynamics

The behavior of individual objects such as atoms has been well understood since the early days of quantum mechanics. However, once these objects begin to interact with each other, a broad range of new physical effects emerge that are of interest for both pure research and technology development. A common approach to studying these effects is to adopt a "bottom up" strategy, where experiments begin by taking a set of simple, isolated quantum objects – individual "spins"—letting them interact, and measuring the states of all of the individual elements in order to obtain insights into the collective behavior. This approach allows for very precise measurement and control, but is limited in scale to ensembles of hundreds or perhaps thousands of elements.

Instead, we adopt a "top down" strategy. We start with a large system and, by controllably introducing disorder, enable the system to self-assemble into a collection of interacting elements. The challenges with this approach lie predominantly in manipulation and addressability. As there are far too many spins to handle individually, we need overall tuning knobs that tie into the small-scale dynamics and local disorder of sets of spins, as well as high resolution probes sensitive to their collective behavior. We choose a family of magnetic crystals that permit us to take advantage of the ability to tune quantum tunneling via a magnetic field applied perpendicular to the ordering direction of the spins. These materials, with random distribution of spins, naturally provide a wide range of size scales and hence a diverse set of collective behaviors.

Entangled quantum state of magnetic dipoles

Free magnetic moments usually manifest themselves in Curie laws, where weak external magnetic fields produce magnetiza- tions that vary as the reciprocal of the temperature (1/T). For a variety of materials that do not display static magnetism, includ- ing doped semiconductors and certain rare-earth intermetallics, the 1/T law is replaced by a power law T^α with α < 1. A much simpler material system—the insulating magnetic salt LiHo_xY_1-xF₄—can also display such a power law. Moreover, comparing the results of numerical simulations of this system with susceptibility and specific-heat data shows that both energy-level splitting and quantum entanglement are crucial to describing its behaviour. The second of these quantum mechanical effects—entanglement, where the wavefunction of a system with several degrees of freedom cannot be written as a product of wavefunctions for each degree of freedom—becomes visible for remarkably small tunnelling terms, and is activated well before tunnelling has visible effects on the spectrum. This finding is significant because it shows that entanglement, rather than energy-level redistribution, can underlie the magnetic behaviour of a simple insulating quantum spin system.

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Entangled quantum state of magnetic dipoles

Coherent spin oscillations in a disordered magnet

Most materials freeze when cooled to sufficiently low temperature. By contrast, we found that magnetic dipoles randomly distributed in a solid matrix condense into a spin liquid with spectral properties on cooling that are the diametric opposite of those for conventional glasses. Measurements of the nonlinear magnetic dynamics in the low-temperature liquid reveal the presence of coherent spin oscillations composed of hundreds of spins with lifetimes of up to 10 seconds. These excitations can be labeled by frequency and manipulated by the magnetic fields from a loop of wire and can permit the encoding of information at multiple frequencies simultaneously.

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Coherent Spin Oscillations in a Disordered Magnet

Coherence and nonlinear dynamics in disordered magnets

Quantum states cohere and interfere. Atoms arranged imperfectly in a solid rarely display these properties. Here we demonstrate an exception in a disordered quantum magnet that divides itself into nearly isolated subsystems. We probe these coherent spin clusters by driving the system nonlinearly and measuring the resulting hole in the linear spectral response. The Fano shape of the hole encodes the incoherent lifetime as well as coherent mixing of the localized excitations. For the Ising magnet, LiHo_0.045Y_0.955F₄, the quality factor Q for spectral holes can be as high as 100,000. We tune the dynamics by sweeping the Fano mixing parameter q through zero via the ac pump amplitude as well as a dc transverse field. The zero-crossing of q is associated with a dissipationless response at the drive frequency. Identifying localized two-level systems in a dense and disordered magnet advances the search for qubit platforms emerging from strongly-interacting, many-body systems.