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arXiv:1109.3796 · Physical Review Letters

Controlling Spin-Spin Network Dynamics by Repeated Projective Measurements

Christian O. Bretschneider, Gonzalo A. Álvarez, Gershon Kurizki, Lucio Frydman

Published Apr 3, 2012• 18 citations
arXivHTMLPDF

Abstract

We show that coupled-spin network manipulations can be made highly effective by repeated projections of the evolving quantum states onto diagonal density-matrix states (populations). As opposed to the intricately crafted pulse trains that are often used to fine-tune a complex network's evolution, the strategy hereby presented derives from the "quantum Zeno effect" and provides a highly robust route to guide the evolution by destroying all unwanted correlations (coherences). We exploit these effects by showing that a relaxationlike behavior is endowed to polarization transfers occurring within a N-spin coupled network. Experimental implementations yield coupling constant determinations for complex spin-coupling topologies, as demonstrated within the field of liquid-state nuclear magnetic resonance.

DOI
10.1103/physrevlett.108.140403

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We show that coupled-spin network manipulations can be made highly effective by repeated projections of the evolving quantum states onto diagonal density-matrix states (populations). As opposed to the intricately crafted pulse trains that are often used to fine-tune a complex network's evolution, the strategy hereby presented derives from the "quantum Zeno effect" and provides a highly robust route to guide the evolution by destroying all unwanted correlations (coherences). We exploit these effects by showing that a relaxationlike behavior is endowed to polarization transfers occurring within a N-spin coupled network. Experimental implementations yield coupling constant determinations for complex spin-coupling topologies, as demonstrated within the field of liquid-state nuclear magnetic resonance.
Finely manipulating a large population of interacting nuclear spins is an extremely challenging problem arising in wide-ranging applications in quantum science and technology. Prominent examples include the design of robust excitation and inversion pulses for nuclear magnetic resonance spectroscopy and imaging, coordination of spin networks for coherence transfer, and control of superposition and entanglement for quantum computation. In this paper, by integrating the technique of small angle approximation with non-harmonic Fourier analysis, we establish a systematic method to construct robust pulse sequences that neutralize the effect of coupling variations in a spin network. In addition, we explore an alternating optimization procedure for tailoring the constructed pulses to satisfy practical design criteria. We also provide numerical examples to demonstrate the efficacy of the proposed methodology.
Repeated observations inhibit the coherent evolution of quantum states through the quantum Zeno effect. In multi-qubit systems this effect provides opportunities to control complex quantum states. Here, we experimentally demonstrate that repeatedly projecting joint observables of multiple spins creates quantum Zeno subspaces and simultaneously suppresses the dephasing caused by a quasi-static environment. We encode up to two logical qubits in these subspaces and show that the enhancement of the dephasing time with increasing number of projections follows a scaling law that is independent of the number of spins involved. These results provide experimental insight into the interplay between frequent multi-spin measurements and slowly varying noise and pave the way for tailoring the dynamics of multi-qubit systems through repeated projections.
We present a method that implements directional, perfect state transfers within a branched spin network by exploiting quantum interferences in the time domain. This method provides a tool for isolating subsystems from a large and complex one. Directionality is achieved by interrupting the spin-spin coupled evolution with periods of free Zeeman evolutions, whose timing is tuned to be commensurate with the relative phases accrued by specific spin pairs. This leads to a resonant transfer between the chosen qubits and to a detuning of all remaining pathways in the network, using only global manipulations. Since the transfer is perfect when the selected pathway is mediated by two or three spins, distant state transfers over complex networks can be achieved by successive recouplings among specific pairs or triads of spins. These effects are illustrated with a quantum simulator involving 13C^{13}\mathrm{C}13C NMR on leucine's backbone; a six-spin network.
In this thesis, we study methods for optimal manipulation of coupled spin dynamics in the presence of relaxation. We use these methods to compute analytical upper bounds for the efficiency of coherence and polarization transfer between coupled nuclear spins in multidimensional nuclear magnetic resonance (NMR) experiments, under the presence of relaxation. We derive relaxation optimized pulse sequences which achieve or approach these bounds and maximize the sensitivity of the experiments. The two systems examined in detail in this thesis, arising in the context of protein NMR spectroscopy, are a coupled heteronuclear spin pair and an Ising spin chain. New schemes for coherence and polarization transfer are found, which yield substantial gains in transfer efficiency, compared to the traditionally used pulse sequences. From the standpoint of mathematical control theory, the problems arising in connection with optimal manipulation of dissipative quantum dynamics, motivate the study of a class of dissipative bilinear control systems and the computation of their reachable sets. For these systems we show that the optimal solution, corresponding to the maximization of transfer efficiency, and the reachable set can be found by solving a semidefinite program.
Relaxation effects impose fundamental limitations on our ability to coherently control quantum mechanical phenomena. In this article, we use principles of optimal control theory to establish physical limits on how closely a quantum mechanical system can be steered to a desired target state in the presence of relaxation. In particular, we explicitly compute the maximum amplitude of coherence or polarization that can be transferred between coupled heteronuclear spins in large molecules at high magnetic fields in the presence of relaxation. Very general decoherence mechanisms that include cross-correlated relaxation have been included in our analysis. We give analytical characterization for the pulse sequences (control laws) that achieve these physical limits and provide supporting experimental evidence. Exploitation of cross-correlation effects has recently led to the development of powerful methods in NMR spectroscopy to study very large biomolecules in solution. For two heteronuclear spins, we demonstrate with experiments that cross-correlated relaxation optimized pulse (CROP) sequences provide significant gains over the state-of-the-art methods. It is shown that despite large relaxation rates, coherence can be transferred between coupled spins without any loss in special cases where cross-correlated relaxation rates can be tuned to autocorrelated relaxation rates.
We experimentally and theoretically demonstrate the purity (polarization) control of qubits entangled with multiple spins, using induced dephasing in nuclear magnetic resonance setups to simulate repeated quantum measurements. We show that one may steer the qubit ensemble towards a quasiequilibrium state of a certain purity by choosing suitable time intervals between dephasing operations. These results demonstrate that repeated dephasing at intervals associated with the anti-Zeno regime leads to ensemble purification, whereas those associated with the Zeno regime lead to ensemble mixing.