# Manipulating system-bath correlations

Manipulations of correlations among quantum systems so as to augment the capabilities of computing and infor- mation processing have been a major focus research in the last decade. In this context manipulations of the dynamics so as to enhance the correlations between coupled quantum systems and overcome their inhomogeneous broadening can be of both fundamental and applied interest. To this end we put forward methods based on repeated unitary phase-shifts (phase modulations) and nonunitary projections on the levels of a readout qubit coupled to a multipartite bath as a novel means of controlling the qubit-bath entanglement. The unitary phase-shifts rephase various quantum interference pathways of the interacting qubit-bath system, thereby avoiding the large inhomogeneities in the bath. By contrast, repeated nonunitary projections momentarily erase the coherences between the coupled systems and subsequently recreate [1, 2] them with larger amplitude. The advantage of this method is that the coupled qubit-bath system reaches a steady state where the information is stored for long times [3].

In order to optimize the process we have put forward a general strategy for dynamic control that ensures bath optimized fidelity of a desired multidimensional quantum operation in the presence of any baths and noises. It benefits from the vast freedom of arbitrary, not just pulsed, timedependent control. This allows the dramatic reduction of the invested energy and the corresponding error compared to pulsed control [4].

As a first novel application of such general, dynamic control of coupled many-body quantum systems, we address a Bose-Einstein Condensate in a doublewell potential. Our theory and experiment provide a means of dynamically controlling decoherence in such systems [5, 6].

The second application of our method is the manipulation of the collective dynamics of spin ensembles that encode a single qubit. Since an ensemble of spins have long coherence times, they can be used as quantum memory. To transfer and retrieve quantum information with high fidelity, we need a perfect quantum talk with the device to which it is coupled, for example a cavity or a superconducting device. Yet the large inhomogeneity in the coupling strengths and the inherent inhomogeneous broadening present in the ensemble of spins impede such quantum talks.

To unmask the effects of inhomogeneities so as to perform perfect quantum operations between the systems one needs an optimized control. The standard spin echo techniques, though proven to be quite successful in correcting the inhomogeneous broadening in certain spin systems, may not suffice. Here we show a nonintuitive method for transferring and retrieving information with high fidelity, by controlling the qubit to which the spin ensemble is coupled. Such a control is much easier than controlling 10^{6} spins in the ensemble by spin echo technique. For finite systems such a method can be used to maximally entangle the qubit with the state of an inhomogeneously broadened spin ensemble, a task impossible using other methods.

We present experimental evidence [2], that the interaction of a qubit with a finite bath of spins can be controlled by coherence destroying random fields that mimic nonunitary projections. By doing such operations one may steer the qubit ensemble towards a desired quasi-equilibrium corresponding to either cooling or heating (increase or decrease in initial purity), by choosing suitable time intervals between nonunitary projections (quantum measurements). These operations repeatedly destroy the qubit-bath correlations (coherences). The counterrotating terms which are usually neglected in the long time limit, can be important at all times under such measurements. This is a first demonstration both theoretically and experimentally, of how the counterrotating terms can determine the long-time saturation value of the qubit state.

The experiments were performed using a liquidstate NMR simulator. The system (*S*) a spin 1/2 nuclear spin of carbon ^{13}C, and the bath was composed of protons. The nonunitary projective measurements on the system are realized by the use of pulsed magnetic field gradients with random energies. Application of such repeated projective measurement eventually takes the total system towards a true steady state, where the total system commutes with the interaction Hamiltonian. Deviations from such a state depend on the relative magnitudes of the rotating and counter-rotating terms.

- [1] N. Erez, G. Gordon, M. Nest, G. Kurizki, Nature 452, 724 (2008).
- [2] Gonzalo A. lvarez, D. D. Bhaktavatsala Rao, Lucio Frydman and Gershon Kurizki, Phys. Rev. Lett. 105, 160401 (2010).
- [3] Goren Gordon, Guy Bensky, David. GelbwaserKlimovsky, D.D. Bhaktavatsala Rao, Noam Erez and Gershon Kurizki. New. J. Phys 11, 12305 (2009).
- [4] J. Clausen, G. Bensky and G. Kurizki, Phys. Rev. Lett. 104, 040401 (2010).
- [5] Y. Khodorkovsky, G. Kurizki, and A. Vardi, Phys. Rev. Lett. 100, 220403 (2008).
- [6] N. BarGill, E. E. Rowen, G. Kurizki, and N. Davidson, Phys. Rev. Lett. 102, 110401 (2009).

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