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Concepts in Magnetic Resonance Part A

Experimental realization of electromagnetically induced transparency in liquid‐state NMR

Louis E. Fernandes, Jennifer T. Choy, Devesh R. Khanal, David G. Cory

Published Sep 1, 2007• 1 citation
Publisher

Abstract

Abstract Quantum interference effects are physical manifestations of the laws of quantum mechanics and provide a tangible link between the microscopic quantum mechanical domain and the macroscopic world that we observe. These phenomena deviate greatly from classical expectations and can be difficult to understand without experimental demonstrations. Here, we suggest an illustrative and accessible means to observe and understand a purely quantum interference effect, electromagnetically induced transparency (EIT), by viewing it from the perspective of quantum information processing (QIP). We also show that NMR, with its accessibility and ability to create pseudo‐pure states suitable for qubit manipulation, is an ideal tool for EIT. This article provides a description of EIT in QIP terms, as well as an experimental demonstration of this effect on an NMR spectrometer. © 2007 Wiley Periodicals, Inc.Concepts Magn Reson Part A 30A: 236–245, 2007.

DOI
10.1002/cmr.a.20095

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Abstract Quantum interference effects are physical manifestations of the laws of quantum mechanics and provide a tangible link between the microscopic quantum mechanical domain and the macroscopic world that we observe. These phenomena deviate greatly from classical expectations and can be difficult to understand without experimental demonstrations. Here, we suggest an illustrative and accessible means to observe and understand a purely quantum interference effect, electromagnetically induced transparency (EIT), by viewing it from the perspective of quantum information processing (QIP). We also show that NMR, with its accessibility and ability to create pseudo‐pure states suitable for qubit manipulation, is an ideal tool for EIT. This article provides a description of EIT in QIP terms, as well as an experimental demonstration of this effect on an NMR spectrometer. © 2007 Wiley Periodicals, Inc.Concepts Magn Reson Part A 30A: 236–245, 2007.
Electromagnetically induced transparency is an effect observed in atomic systems, originating from quantum interference, in which electromagnetic transitions to and from a certain quantum state become suppressed. This dark state is also characterized by a quantum phase, relative to other states, which theoretically should stop evolving, but remain phase coherent, during transparency. We test this theoretical prediction using techniques developed for liquid-state nuclear magnetic resonance quantum computation, applied to a spin-7/2 nuclear spin system. A sequence of quantum operations is applied to create the dark state, and during transparency its phase evolution is measured relative to a reference state using Ramsey interferometry. Experimental measurements of the fringe visibility are in excellent agreement with theoretical expectations, taking into account measured decoherence rates.
After a general introduction to nuclear magnetic resonance (NMR), we give the basics of implementing quantum algorithms. We describe how qubits are realized and controlled with RF pulses, their internal interactions, and gradient fields. A peculiarity of NMR is that the internal interactions (given by the internal Hamiltonian) are always on. We discuss how they can be effectively turned off with the help of a standard NMR method called ``refocusing''. Liquid state NMR experiments are done at room temperature, leading to an extremely mixed (that is, nearly random) initial state. Despite this high degree of randomness, it is possible to investigate QIP because the relaxation time (the time scale over which useful signal from a computation is lost) is sufficiently long. We explain how this feature leads to the crucial ability of simulating a pure (non-random) state by using ``pseudopure'' states. We discuss how the ``answer'' provided by a computation is obtained by measurement and how this measurement differs from the ideal, projective measurement of QIP. We then give implementations of some simple quantum algorithms with a typical experimental result. We conclude with a discussion of what we have learned from NMR QIP so far and what the prospects for future NMR QIP experiments are.
Nuclear magnetic resonance (NMR) provides an experimental setting to explore physical implementations of quantum information processing (QIP). Here we introduce the basic background for understanding applications of NMR to QIP and explain their current successes, limitations and potential. NMR spectroscopy is well known for its wealth of diverse coherent manipulations of spin dynamics. Ideas and instrumentation from liquid state NMR spectroscopy have been used to experiment with QIP. This approach has carried the field to a complexity of about 10 qubits, a small number for quantum computation but large enough for observing and better understanding the complexity of the quantum world. While liquid state NMR is the only present-day technology about to reach this number of qubits, further increases in complexity will require new methods. We sketch one direction leading towards a scalable quantum computer using spin 1/2 particles. The next step of which is a solid state NMR-based QIP capable of reaching 10—30 qubits.
Induced transparency, an interference effect due to mode coupling, has attracted significant research interest. The first discovered and most striking type of induced transparency plays electromagnetically induced transparency (EIT) in atomic systems. Optical cavities serve as a more ideal and feasible platform for realizing the effects of induced transparency, which leads to considerable demonstrations in theory and experiments. This review provides a run‐through of research findings on different types of induced transparency phenomenon, including, inter alia, EIT, optomechanically induced transparency, plasmon‐induced transparency, Brillouin scattering induced transparency, optically induced transparency, photothermally induced transparency, and dipole‐induced transparency. Their mechanisms, developments, techniques, and applications are discussed in detail. Most importantly, the emerging area of induced transparency at exceptional points is analyzed for its great promise. The last section presents a brief summary and perspective of induced transparency with optical cavities.
Nuclear magnetic resonance (NMR) is a direct macroscopic manifestation of the quantum mechanics of the intrinsic angular momentum of atomic nuclei. It is best known for its extraordinary range of applications, which include molecular structure determination, medical imaging, and measurements of flow and diffusion rates. Most recently, liquid-state NMR spectroscopy has been found to provide a powerful experimental tool for the development and evaluation of the coherent control techniques needed for quantum information processing. This burgeoning new interdisciplinary field has the potential to achieve cryptographic, communications, and computational feats far beyond what is possible with known classical physics. Indeed, NMR has made the demonstration of many of these feats sufficiently simple to be carried out by high school summer interns working in our laboratory (see the last two authors). In this paper the basic principles of quantum information processing by NMR spectroscopy are described, along with several illustrative experiments suitable for incorporation into the undergraduate physics curriculum. These experiments are spin–spin interferometry, an implementation of the quantum Fourier transform, and the quantum simulation of a harmonic oscillator.