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arXiv:0809.2993 · Physical Review Letters

Engineering Giant Nonlinearities in Quantum Nanosystems

Kurt A. Jacobs, Andrew J. Landahl

Published Aug 5, 2009• 69 citations
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Abstract

We describe a method to engineer giant nonlinearities in, and probes to measure nonlinear observables of, mesoscopic quantum resonators. This involves tailoring the Hamiltonian of a simple auxiliary system perturbatively coupled to the resonator, and has the potential to engineer a wide range of nonlinearities to high accuracy. We give a number of explicit examples, including a readily realizable two-qubit auxiliary system that creates an x;{4} potential and a chi;{(3)} (Kerr) nonlinearity, valid to fifth order in the perturbative coupling.

DOI
10.1103/physrevlett.103.067201

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We describe a method to engineer giant nonlinearities in, and probes to measure nonlinear observables of, mesoscopic quantum resonators. This involves tailoring the Hamiltonian of a simple auxiliary system perturbatively coupled to the resonator, and has the potential to engineer a wide range of nonlinearities to high accuracy. We give a number of explicit examples, including a readily realizable two-qubit auxiliary system that creates an x;{4} potential and a chi;{(3)} (Kerr) nonlinearity, valid to fifth order in the perturbative coupling.
We predict that the effective nonlinear optical susceptibility can be tailored using the Purcell effect. While this is a general physical principle that applies to a wide variety of nonlinearities, we specifically investigate the Kerr nonlinearity. We show theoretically that using the Purcell effect for frequencies close to an atomic resonance can substantially influence the resultant Kerr nonlinearity for light of all (even highly detuned) frequencies. For example, in realistic physical systems, enhancement of the Kerr coefficient by one to two orders of magnitude could be achieved.
A scheme for giant enhancement of the Kerr nonlinearity in linear triple quantum dot molecules is proposed. In such a system, the tunneling-induced transparency window obtained in double quantum dot molecules splits into two windows, due to the coupling with the third quantum dot. And most important, the Kerr nonlinearity can be enhanced by several orders of magnitude, compared with that generated in double quantum dot molecules. With proper detuning of the tunneling, giant Kerr nonlinearity accompanied by vanishing absorption can be realized, which opens the possibility to enhance self-phase modulation in tunneling controllable semiconductor nanostructures under conditions of low light levels. Quantitative analysis shows that the giant Kerr nonlinearity is attributed to the interacting double dark resonances induced by the tunneling between the triple quantum dots, therefore no extra laser fields are required.
We show that a nanoresonator can be prepared in mesoscopic superposition states merely by monitoring a qubit coupled to the square of the resonator's position. This works for thermal initial states, and does not require a third-order nonlinearity. The required coupling can be generated using a simple open-loop control protocol, obtained with optimal control theory. We simulate the complete preparation process, including environmental noise. Our results indicate the power of open-loop control for state engineering and measurement in quantum nanosystems.
We propose a scheme to realize a cubic quantum nondemolition (QND) Hamiltonian with optical parametric interactions. We show that strongly squeezed fundamental and second-harmonic fields propagating in a χ (2) nonlinear medium effectively evolve under a cubic QND Hamiltonian. We highlight the versatility offered by such a Hamiltonian for engineering non-Gaussian quantum states, such as Schrödinger cat states and cubic phase states. We show that our scheme can be highly tolerant of overall detection inefficiency with an auxiliary high-gain phase-sensitive optical amplifier. Our proposal involves parametric interactions in a mesoscopic photon-number regime, significantly enhancing the effective nonlinear coupling from the native single-photon coupling rate while providing powerful means to fight photon propagation loss. Experimental numbers suggest that our scheme might be feasible in the near future, particularly with pulsed nonlinear nanophotonics.