Bandwidth-limited control and ringdown suppression in high-Q resonators.

We describe how the transient behavior of a tuned and matched resonator circuit and a ringdown suppression pulse may be integrated into an optimal control theory (OCT) pulse-design algorithm to derive control sequences with limited ringdown that perform a desired quantum operation in the presence of resonator distortions of the ideal waveform. Inclusion of ringdown suppression in numerical pulse optimizations significantly reduces spectrometer deadtime when using high quality factor (high-Q) resonators, leading to increased signal-to-noise ratio (SNR) and sensitivity of inductive measurements. To demonstrate the method, we experimentally measure the free-induction decay of an inhomogeneously broadened solid-state free radical spin system at high Q. The measurement is enabled by using a numerically optimized bandwidth-limited OCT pulse, including ringdown suppression, robust to variations in static and microwave field strengths. We also discuss the applications of pulse design in high-Q resonators to universal control of anisotropic-hyperfine coupled electron-nuclear spin systems via electron-only modulation even when the bandwidth of the resonator is significantly smaller than the hyperfine coupling strength. These results demonstrate how limitations imposed by linear response theory may be vastly exceeded when using a sufficiently accurate system model to optimize pulses of high complexity.

[1]  Richard W Quine,et al.  Digital EPR with an arbitrary waveform generator and direct detection at the carrier frequency. , 2011, Journal of magnetic resonance.

[2]  David G. Cory,et al.  A generalized k-space formalism for treating the spatial aspects of a variety of NMR experiments , 1998 .

[3]  Ramakrishna,et al.  Controllability of molecular systems. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[4]  M. Mehring,et al.  Phase Transients in Pulsed NMR Spectrometers , 1972 .

[5]  A. L. Kwiram,et al.  ENDOR Studies at 4.2 K of the Radicals in Malonic Acid Single Crystals. , 1993 .

[6]  D. D’Alessandro.  Introduction to Quantum Control and Dynamics , 2007 .

[7]  Michael Levit,et al.  High-sensitivity Q-band electron spin resonance imaging system with submicron resolution. , 2011, The Review of scientific instruments.

[8]  Navin Khaneja,et al.  Switched control of electron nuclear spin systems , 2007, 0707.1572.

[9]  H. Carr,et al.  The Principles of Nuclear Magnetism , 1961 .

[11]  J. M. Gambetta,et al.  Optimal control methods for rapidly time-varying Hamiltonians , 2011, 1102.0584.

[12]  A. I. Solomon,et al.  Complete controllability of quantum systems , 2000, quant-ph/0010031.

[13]  M. Mehring,et al.  Elimination of ringing effects in multiple-pulse sequences , 1990 .

[14]  D G Cory,et al.  Parallel information transfer in a multinode quantum information processor. , 2012, Physical review letters.

[15]  T. Umeda,et al.  Electron spin resonance detected by a superconducting qubit , 2012, 1205.5659.

[16]  Daniel D. Elleman,et al.  A Simple, Low Power, Multiple Pulse NMR Spectrometer , 1972 .

[17]  S Lloyd,et al.  A Potentially Realizable Quantum Computer , 1993, Science.

[18]  D. Hoult.  The solution of the bloch equations in the presence of a varying B1 field—An approach to selective pulse analysis , 1979 .

[19]  G. Rinard,et al.  Frequency Dependence of EPR Sensitivity , 2004 .

[20]  Raymond Laflamme,et al.  Demonstration of sufficient control for two rounds of quantum error correction in a solid state ensemble quantum information processor. , 2011, Physical review letters.

[21]  R. Kubo,et al.  A General Theory Of Magnetic Resonance Absorption , 1954 .

[22]  J. Freed,et al.  Composite pulses in time-domain ESR , 1989 .

[23]  A. Houck,et al.  Superconducting coplanar waveguide resonators for low temperature pulsed electron spin resonance spectroscopy. , 2012, The Review of scientific instruments.

[24]  J. Freed,et al.  Spectral rotation in pulsed ESR spectroscopy , 1986 .

[25]  Gunnar Jeschke,et al.  Principles of pulse electron paramagnetic resonance , 2001 .

[26]  M Negoro,et al.  Total compensation of pulse transients inside a resonator. , 2010, Journal of magnetic resonance.

[27]  M. Mehring,et al.  Indirect detection of selective nuclear spin-spin interactions in a hostile environment. , 2006, Solid state nuclear magnetic resonance.

[28]  Timo O. Reiss,et al.  Optimal control of coupled spin dynamics: design of NMR pulse sequences by gradient ascent algorithms. , 2005, Journal of magnetic resonance.

[29]  Jean Jeener,et al.  Suppression of Radiation Damping in NMR in Liquids by Active Electronic Feedback , 1995 .

[30]  Jonathan Stuart Hodges.  Engineering coherent control of quantum information in spin systems , 2007 .

[31]  Raymond Laflamme,et al.  Coherent control of two nuclear spins using the anisotropic hyperfine interaction. , 2011, Physical review letters.

[32]  Aharon Blank,et al.  ESR imaging in solid phase down to sub-micron resolution: methodology and applications. , 2009, Physical chemistry chemical physics : PCCP.

[33]  Fedor Jelezko,et al.  Single defect centres in diamond: A review , 2006 .

[34]  D G Cory,et al.  Superconducting microstrip resonator for pulsed ESR of thin films. , 2013, Journal of magnetic resonance.

[35]  A. V. Gorshkov,et al.  Scalable architecture for a room temperature solid-state quantum information processor , 2010, Nature Communications.

[36]  P Cappellaro,et al.  Coherence and control of quantum registers based on electronic spin in a nuclear spin bath. , 2009, Physical review letters.

[37]  S. Eaton,et al.  Irradiated Fused-Quartz Standard Sample for Time-Domain EPR , 1993 .

[38]  Michael Mehring,et al.  Principles of high-resolution NMR in solids , 1982 .

[39]  David G. Cory,et al.  Universal control of nuclear spins via anisotropic hyperfine interactions , 2007 .

[40]  David G Cory,et al.  Application of optimal control to CPMG refocusing pulse design. , 2010, Journal of magnetic resonance.

[41]  Michael Mehring,et al.  Spin-bus concept of spin quantum computing , 2006 .

[42]  Timothy F. Havel,et al.  Design of strongly modulating pulses to implement precise effective Hamiltonians for quantum information processing , 2002, quant-ph/0202065.

[43]  D I Hoult,et al.  Fast recovery, high sensitivity NMR probe and preamplifier for low frequencies. , 1979, The Review of scientific instruments.

[44]  Ray Freeman,et al.  Selective excitation in Fourier transform nuclear magnetic resonance. 1978. , 1978, Journal of magnetic resonance.

[45]  A. Blank,et al.  Note: High sensitivity pulsed electron spin resonance spectroscopy with induction detection. , 2011, The Review of scientific instruments.

[46]  R. Quine,et al.  A signal-to-noise standard for pulsed EPR. , 2010, Journal of magnetic resonance.

[47]  M. Chial,et al.  in simple , 2003 .

[48]  E. Knill,et al.  Liquid-state nuclear magnetic resonance as a testbed for developing quantum control methods , 2008, 0803.1982.

[49]  Joel F Martin,et al.  Phase transients in NMR probe circuits , 1991 .

[50]  Timothy F. Havel,et al.  Robust control of quantum information , 2003, quant-ph/0307062.

[51]  M. L. Chambers.  The Mathematical Theory of Optimal Processes , 1965 .

[52]  L. S. Pontryagin,et al.  Mathematical Theory of Optimal Processes , 1962 .

[53]  Raymond Laflamme,et al.  Fidelity enhancement by logical qubit encoding. , 2007, Physical review letters.

[54]  Steffen J Glaser,et al.  Shaped optimal control pulses for increased excitation bandwidth in EPR. , 2012, Journal of magnetic resonance.

[55]  W. Froncisz,et al.  Relative Benefits of Overcoupled Resonators vs Inherently Low-Q Resonators for Pulsed Magnetic Resonance , 1994 .

[56]  R J Schoelkopf,et al.  Quantum computing with an electron spin ensemble. , 2009, Physical review letters.

[57]  Timothy F. Havel,et al.  Incoherent noise and quantum information processing. , 2003, The Journal of chemical physics.

[58]  A. J. Vega.  Controlling the effects of pulse transients and RF inhomogeneity in phase-modulated multiple-pulse sequences for homonuclear decoupling in solid-state proton NMR. , 2004, Journal of magnetic resonance.