Abstract

We discuss the unique capabilities of programmable logic devices (PLDs) for experimental quantum optics and describe basic procedures of design and implementation. Examples of advanced applications include optical metrology and feedback control of quantum dynamical systems. As a tutorial illustration of the PLD implementation process, a field-programmable gate array controller is used to stabilize the output of a Fabry-Perot cavity.

© 2002 Optical Society of America

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  1. C. A. Sackett, D. Kielpinski, B. E. King, C. Langer, V. Meyer, C. J. Myatt, M. Rowe, Q. A. Turchette, W. M. Itano, D. J. Wineland, and C. Monroe, “Experimental entanglement of four particles,” Nature 404, 256–259 (2000).
    [CrossRef] [PubMed]
  2. M. R. Andrews, M.-O. Mewes, N. J. van Druten, D. S. Durfee, D. M. Kurn, and W. Ketterle, “Direct, nondestructive observation of a Bose condensate,” Science 273, 84–87 (1996).
    [CrossRef] [PubMed]
  3. C. J. Hood, T. W. Lynn, A. C. Doherty, A. S. Parkins, and H. J. Kimble, “The atom-cavity microscope: single atoms bound in orbit by single photons,” Science 287, 1447–1453 (2000).
    [CrossRef] [PubMed]
  4. A. C. Doherty, S. Habib, K. Jacobs, H. Mabuchi, and S. M. Tan, “Quantum feedback control and classical control theory,” Phys. Rev. A 62, 012105 (2000).
    [CrossRef]
  5. H. M. Wiseman and R. B. Killip, “Adaptive single-shot phase measurements: the full quantum theory,” Phys. Rev. A 57, 2169–2185 (1998).
    [CrossRef]
  6. B. Rahn, A. C. Doherty, and H. Mabuchi, “Exact performance of concatenated quantum codes,” Phys. Rev. A 66, 032304 (2002).
    [CrossRef]
  7. A. C. Doherty, P. A. Parrilo, and F. M. Spedalieri, “Distinguishing separable and entangled states,” Phys. Rev. Lett. 88, 187904 (2002).
    [CrossRef] [PubMed]
  8. M. E. Cseta and J. C. Doyle, “Reverse engineering of biological complexity,” Science 295, 1664–1669 (2002).
    [CrossRef]
  9. O. L. R. Jacobs, Introduction to Control Theory (Oxford University, Oxford, UK, 1993).
  10. M. A. Armen, J. K. Au, J. K. Stockton, A. C. Doherty, and H. Mabuchi, “Adaptive homodyne measurement of optical phase,” Phys. Rev. Lett. 89, 133602 (2002).
    [CrossRef] [PubMed]
  11. S. Habib, habib@lanl.gov, K. Jacobs, and H. Mabuchi are preparing a manuscript to be called “Feedback control of atomic motion in an optical cavity.”
  12. H. Rabitz, R. de Vivie-Riedle, M. Motzkus, and K. Kompa, “Whither the future of controlling quantum phenomena?,” Science 288, 824–828 (2000).
    [CrossRef] [PubMed]
  13. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University, Cambridge, UK, 2000).
  14. D. Stranneby, Digital Signal Processing: DSP and Applications (Newnes, Oxford, UK, 2001).

2002

B. Rahn, A. C. Doherty, and H. Mabuchi, “Exact performance of concatenated quantum codes,” Phys. Rev. A 66, 032304 (2002).
[CrossRef]

A. C. Doherty, P. A. Parrilo, and F. M. Spedalieri, “Distinguishing separable and entangled states,” Phys. Rev. Lett. 88, 187904 (2002).
[CrossRef] [PubMed]

M. E. Cseta and J. C. Doyle, “Reverse engineering of biological complexity,” Science 295, 1664–1669 (2002).
[CrossRef]

M. A. Armen, J. K. Au, J. K. Stockton, A. C. Doherty, and H. Mabuchi, “Adaptive homodyne measurement of optical phase,” Phys. Rev. Lett. 89, 133602 (2002).
[CrossRef] [PubMed]

2000

H. Rabitz, R. de Vivie-Riedle, M. Motzkus, and K. Kompa, “Whither the future of controlling quantum phenomena?,” Science 288, 824–828 (2000).
[CrossRef] [PubMed]

C. A. Sackett, D. Kielpinski, B. E. King, C. Langer, V. Meyer, C. J. Myatt, M. Rowe, Q. A. Turchette, W. M. Itano, D. J. Wineland, and C. Monroe, “Experimental entanglement of four particles,” Nature 404, 256–259 (2000).
[CrossRef] [PubMed]

C. J. Hood, T. W. Lynn, A. C. Doherty, A. S. Parkins, and H. J. Kimble, “The atom-cavity microscope: single atoms bound in orbit by single photons,” Science 287, 1447–1453 (2000).
[CrossRef] [PubMed]

A. C. Doherty, S. Habib, K. Jacobs, H. Mabuchi, and S. M. Tan, “Quantum feedback control and classical control theory,” Phys. Rev. A 62, 012105 (2000).
[CrossRef]

1998

H. M. Wiseman and R. B. Killip, “Adaptive single-shot phase measurements: the full quantum theory,” Phys. Rev. A 57, 2169–2185 (1998).
[CrossRef]

1996

M. R. Andrews, M.-O. Mewes, N. J. van Druten, D. S. Durfee, D. M. Kurn, and W. Ketterle, “Direct, nondestructive observation of a Bose condensate,” Science 273, 84–87 (1996).
[CrossRef] [PubMed]

Andrews, M. R.

M. R. Andrews, M.-O. Mewes, N. J. van Druten, D. S. Durfee, D. M. Kurn, and W. Ketterle, “Direct, nondestructive observation of a Bose condensate,” Science 273, 84–87 (1996).
[CrossRef] [PubMed]

Armen, M. A.

M. A. Armen, J. K. Au, J. K. Stockton, A. C. Doherty, and H. Mabuchi, “Adaptive homodyne measurement of optical phase,” Phys. Rev. Lett. 89, 133602 (2002).
[CrossRef] [PubMed]

Au, J. K.

M. A. Armen, J. K. Au, J. K. Stockton, A. C. Doherty, and H. Mabuchi, “Adaptive homodyne measurement of optical phase,” Phys. Rev. Lett. 89, 133602 (2002).
[CrossRef] [PubMed]

Cseta, M. E.

M. E. Cseta and J. C. Doyle, “Reverse engineering of biological complexity,” Science 295, 1664–1669 (2002).
[CrossRef]

de Vivie-Riedle, R.

H. Rabitz, R. de Vivie-Riedle, M. Motzkus, and K. Kompa, “Whither the future of controlling quantum phenomena?,” Science 288, 824–828 (2000).
[CrossRef] [PubMed]

Doherty, A. C.

M. A. Armen, J. K. Au, J. K. Stockton, A. C. Doherty, and H. Mabuchi, “Adaptive homodyne measurement of optical phase,” Phys. Rev. Lett. 89, 133602 (2002).
[CrossRef] [PubMed]

B. Rahn, A. C. Doherty, and H. Mabuchi, “Exact performance of concatenated quantum codes,” Phys. Rev. A 66, 032304 (2002).
[CrossRef]

A. C. Doherty, P. A. Parrilo, and F. M. Spedalieri, “Distinguishing separable and entangled states,” Phys. Rev. Lett. 88, 187904 (2002).
[CrossRef] [PubMed]

A. C. Doherty, S. Habib, K. Jacobs, H. Mabuchi, and S. M. Tan, “Quantum feedback control and classical control theory,” Phys. Rev. A 62, 012105 (2000).
[CrossRef]

C. J. Hood, T. W. Lynn, A. C. Doherty, A. S. Parkins, and H. J. Kimble, “The atom-cavity microscope: single atoms bound in orbit by single photons,” Science 287, 1447–1453 (2000).
[CrossRef] [PubMed]

Doyle, J. C.

M. E. Cseta and J. C. Doyle, “Reverse engineering of biological complexity,” Science 295, 1664–1669 (2002).
[CrossRef]

Durfee, D. S.

M. R. Andrews, M.-O. Mewes, N. J. van Druten, D. S. Durfee, D. M. Kurn, and W. Ketterle, “Direct, nondestructive observation of a Bose condensate,” Science 273, 84–87 (1996).
[CrossRef] [PubMed]

Habib, S.

A. C. Doherty, S. Habib, K. Jacobs, H. Mabuchi, and S. M. Tan, “Quantum feedback control and classical control theory,” Phys. Rev. A 62, 012105 (2000).
[CrossRef]

Hood, C. J.

C. J. Hood, T. W. Lynn, A. C. Doherty, A. S. Parkins, and H. J. Kimble, “The atom-cavity microscope: single atoms bound in orbit by single photons,” Science 287, 1447–1453 (2000).
[CrossRef] [PubMed]

Itano, W. M.

C. A. Sackett, D. Kielpinski, B. E. King, C. Langer, V. Meyer, C. J. Myatt, M. Rowe, Q. A. Turchette, W. M. Itano, D. J. Wineland, and C. Monroe, “Experimental entanglement of four particles,” Nature 404, 256–259 (2000).
[CrossRef] [PubMed]

Jacobs, K.

A. C. Doherty, S. Habib, K. Jacobs, H. Mabuchi, and S. M. Tan, “Quantum feedback control and classical control theory,” Phys. Rev. A 62, 012105 (2000).
[CrossRef]

Ketterle, W.

M. R. Andrews, M.-O. Mewes, N. J. van Druten, D. S. Durfee, D. M. Kurn, and W. Ketterle, “Direct, nondestructive observation of a Bose condensate,” Science 273, 84–87 (1996).
[CrossRef] [PubMed]

Kielpinski, D.

C. A. Sackett, D. Kielpinski, B. E. King, C. Langer, V. Meyer, C. J. Myatt, M. Rowe, Q. A. Turchette, W. M. Itano, D. J. Wineland, and C. Monroe, “Experimental entanglement of four particles,” Nature 404, 256–259 (2000).
[CrossRef] [PubMed]

Killip, R. B.

H. M. Wiseman and R. B. Killip, “Adaptive single-shot phase measurements: the full quantum theory,” Phys. Rev. A 57, 2169–2185 (1998).
[CrossRef]

Kimble, H. J.

C. J. Hood, T. W. Lynn, A. C. Doherty, A. S. Parkins, and H. J. Kimble, “The atom-cavity microscope: single atoms bound in orbit by single photons,” Science 287, 1447–1453 (2000).
[CrossRef] [PubMed]

King, B. E.

C. A. Sackett, D. Kielpinski, B. E. King, C. Langer, V. Meyer, C. J. Myatt, M. Rowe, Q. A. Turchette, W. M. Itano, D. J. Wineland, and C. Monroe, “Experimental entanglement of four particles,” Nature 404, 256–259 (2000).
[CrossRef] [PubMed]

Kompa, K.

H. Rabitz, R. de Vivie-Riedle, M. Motzkus, and K. Kompa, “Whither the future of controlling quantum phenomena?,” Science 288, 824–828 (2000).
[CrossRef] [PubMed]

Kurn, D. M.

M. R. Andrews, M.-O. Mewes, N. J. van Druten, D. S. Durfee, D. M. Kurn, and W. Ketterle, “Direct, nondestructive observation of a Bose condensate,” Science 273, 84–87 (1996).
[CrossRef] [PubMed]

Langer, C.

C. A. Sackett, D. Kielpinski, B. E. King, C. Langer, V. Meyer, C. J. Myatt, M. Rowe, Q. A. Turchette, W. M. Itano, D. J. Wineland, and C. Monroe, “Experimental entanglement of four particles,” Nature 404, 256–259 (2000).
[CrossRef] [PubMed]

Lynn, T. W.

C. J. Hood, T. W. Lynn, A. C. Doherty, A. S. Parkins, and H. J. Kimble, “The atom-cavity microscope: single atoms bound in orbit by single photons,” Science 287, 1447–1453 (2000).
[CrossRef] [PubMed]

Mabuchi, H.

B. Rahn, A. C. Doherty, and H. Mabuchi, “Exact performance of concatenated quantum codes,” Phys. Rev. A 66, 032304 (2002).
[CrossRef]

M. A. Armen, J. K. Au, J. K. Stockton, A. C. Doherty, and H. Mabuchi, “Adaptive homodyne measurement of optical phase,” Phys. Rev. Lett. 89, 133602 (2002).
[CrossRef] [PubMed]

A. C. Doherty, S. Habib, K. Jacobs, H. Mabuchi, and S. M. Tan, “Quantum feedback control and classical control theory,” Phys. Rev. A 62, 012105 (2000).
[CrossRef]

Mewes, M.-O.

M. R. Andrews, M.-O. Mewes, N. J. van Druten, D. S. Durfee, D. M. Kurn, and W. Ketterle, “Direct, nondestructive observation of a Bose condensate,” Science 273, 84–87 (1996).
[CrossRef] [PubMed]

Meyer, V.

C. A. Sackett, D. Kielpinski, B. E. King, C. Langer, V. Meyer, C. J. Myatt, M. Rowe, Q. A. Turchette, W. M. Itano, D. J. Wineland, and C. Monroe, “Experimental entanglement of four particles,” Nature 404, 256–259 (2000).
[CrossRef] [PubMed]

Monroe, C.

C. A. Sackett, D. Kielpinski, B. E. King, C. Langer, V. Meyer, C. J. Myatt, M. Rowe, Q. A. Turchette, W. M. Itano, D. J. Wineland, and C. Monroe, “Experimental entanglement of four particles,” Nature 404, 256–259 (2000).
[CrossRef] [PubMed]

Motzkus, M.

H. Rabitz, R. de Vivie-Riedle, M. Motzkus, and K. Kompa, “Whither the future of controlling quantum phenomena?,” Science 288, 824–828 (2000).
[CrossRef] [PubMed]

Myatt, C. J.

C. A. Sackett, D. Kielpinski, B. E. King, C. Langer, V. Meyer, C. J. Myatt, M. Rowe, Q. A. Turchette, W. M. Itano, D. J. Wineland, and C. Monroe, “Experimental entanglement of four particles,” Nature 404, 256–259 (2000).
[CrossRef] [PubMed]

Parkins, A. S.

C. J. Hood, T. W. Lynn, A. C. Doherty, A. S. Parkins, and H. J. Kimble, “The atom-cavity microscope: single atoms bound in orbit by single photons,” Science 287, 1447–1453 (2000).
[CrossRef] [PubMed]

Parrilo, P. A.

A. C. Doherty, P. A. Parrilo, and F. M. Spedalieri, “Distinguishing separable and entangled states,” Phys. Rev. Lett. 88, 187904 (2002).
[CrossRef] [PubMed]

Rabitz, H.

H. Rabitz, R. de Vivie-Riedle, M. Motzkus, and K. Kompa, “Whither the future of controlling quantum phenomena?,” Science 288, 824–828 (2000).
[CrossRef] [PubMed]

Rahn, B.

B. Rahn, A. C. Doherty, and H. Mabuchi, “Exact performance of concatenated quantum codes,” Phys. Rev. A 66, 032304 (2002).
[CrossRef]

Rowe, M.

C. A. Sackett, D. Kielpinski, B. E. King, C. Langer, V. Meyer, C. J. Myatt, M. Rowe, Q. A. Turchette, W. M. Itano, D. J. Wineland, and C. Monroe, “Experimental entanglement of four particles,” Nature 404, 256–259 (2000).
[CrossRef] [PubMed]

Sackett, C. A.

C. A. Sackett, D. Kielpinski, B. E. King, C. Langer, V. Meyer, C. J. Myatt, M. Rowe, Q. A. Turchette, W. M. Itano, D. J. Wineland, and C. Monroe, “Experimental entanglement of four particles,” Nature 404, 256–259 (2000).
[CrossRef] [PubMed]

Spedalieri, F. M.

A. C. Doherty, P. A. Parrilo, and F. M. Spedalieri, “Distinguishing separable and entangled states,” Phys. Rev. Lett. 88, 187904 (2002).
[CrossRef] [PubMed]

Stockton, J. K.

M. A. Armen, J. K. Au, J. K. Stockton, A. C. Doherty, and H. Mabuchi, “Adaptive homodyne measurement of optical phase,” Phys. Rev. Lett. 89, 133602 (2002).
[CrossRef] [PubMed]

Tan, S. M.

A. C. Doherty, S. Habib, K. Jacobs, H. Mabuchi, and S. M. Tan, “Quantum feedback control and classical control theory,” Phys. Rev. A 62, 012105 (2000).
[CrossRef]

Turchette, Q. A.

C. A. Sackett, D. Kielpinski, B. E. King, C. Langer, V. Meyer, C. J. Myatt, M. Rowe, Q. A. Turchette, W. M. Itano, D. J. Wineland, and C. Monroe, “Experimental entanglement of four particles,” Nature 404, 256–259 (2000).
[CrossRef] [PubMed]

van Druten, N. J.

M. R. Andrews, M.-O. Mewes, N. J. van Druten, D. S. Durfee, D. M. Kurn, and W. Ketterle, “Direct, nondestructive observation of a Bose condensate,” Science 273, 84–87 (1996).
[CrossRef] [PubMed]

Wineland, D. J.

C. A. Sackett, D. Kielpinski, B. E. King, C. Langer, V. Meyer, C. J. Myatt, M. Rowe, Q. A. Turchette, W. M. Itano, D. J. Wineland, and C. Monroe, “Experimental entanglement of four particles,” Nature 404, 256–259 (2000).
[CrossRef] [PubMed]

Wiseman, H. M.

H. M. Wiseman and R. B. Killip, “Adaptive single-shot phase measurements: the full quantum theory,” Phys. Rev. A 57, 2169–2185 (1998).
[CrossRef]

Nature

C. A. Sackett, D. Kielpinski, B. E. King, C. Langer, V. Meyer, C. J. Myatt, M. Rowe, Q. A. Turchette, W. M. Itano, D. J. Wineland, and C. Monroe, “Experimental entanglement of four particles,” Nature 404, 256–259 (2000).
[CrossRef] [PubMed]

Phys. Rev. A

A. C. Doherty, S. Habib, K. Jacobs, H. Mabuchi, and S. M. Tan, “Quantum feedback control and classical control theory,” Phys. Rev. A 62, 012105 (2000).
[CrossRef]

H. M. Wiseman and R. B. Killip, “Adaptive single-shot phase measurements: the full quantum theory,” Phys. Rev. A 57, 2169–2185 (1998).
[CrossRef]

B. Rahn, A. C. Doherty, and H. Mabuchi, “Exact performance of concatenated quantum codes,” Phys. Rev. A 66, 032304 (2002).
[CrossRef]

Phys. Rev. Lett.

A. C. Doherty, P. A. Parrilo, and F. M. Spedalieri, “Distinguishing separable and entangled states,” Phys. Rev. Lett. 88, 187904 (2002).
[CrossRef] [PubMed]

M. A. Armen, J. K. Au, J. K. Stockton, A. C. Doherty, and H. Mabuchi, “Adaptive homodyne measurement of optical phase,” Phys. Rev. Lett. 89, 133602 (2002).
[CrossRef] [PubMed]

Science

M. R. Andrews, M.-O. Mewes, N. J. van Druten, D. S. Durfee, D. M. Kurn, and W. Ketterle, “Direct, nondestructive observation of a Bose condensate,” Science 273, 84–87 (1996).
[CrossRef] [PubMed]

C. J. Hood, T. W. Lynn, A. C. Doherty, A. S. Parkins, and H. J. Kimble, “The atom-cavity microscope: single atoms bound in orbit by single photons,” Science 287, 1447–1453 (2000).
[CrossRef] [PubMed]

M. E. Cseta and J. C. Doyle, “Reverse engineering of biological complexity,” Science 295, 1664–1669 (2002).
[CrossRef]

H. Rabitz, R. de Vivie-Riedle, M. Motzkus, and K. Kompa, “Whither the future of controlling quantum phenomena?,” Science 288, 824–828 (2000).
[CrossRef] [PubMed]

Other

M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University, Cambridge, UK, 2000).

D. Stranneby, Digital Signal Processing: DSP and Applications (Newnes, Oxford, UK, 2001).

O. L. R. Jacobs, Introduction to Control Theory (Oxford University, Oxford, UK, 1993).

S. Habib, habib@lanl.gov, K. Jacobs, and H. Mabuchi are preparing a manuscript to be called “Feedback control of atomic motion in an optical cavity.”

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Figures (8)

Fig. 1
Fig. 1

Antiharmonic-oscillator (AHO) transfer function is designed such that its product with the harmonic-oscillator (HO) transfer function equals that of an integrator with a constant -90° phase.

Fig. 2
Fig. 2

Amplitude response and delay of the entire GV-290 board (ADC→FPGA→DAC). Note that the delay below the Nyquist frequency (fC/2=50 MHz) is ∼160 ns. The phase response in the constant delay region is linear with slope proportional to the delay.

Fig. 3
Fig. 3

FPGA schematic and corresponding code for the adaptive phase measurement algorithm. In the schematic the process is not represented as a block component because it is coded in a serial manner.

Fig. 4
Fig. 4

Φ(t) and I(t) trajectories for the phase measurement of a single pulse of light. The current is locked to zero and the ending point of the phase is a rough estimate of the measured phase. The true phase measurement is a functional of both traces. The oscillations are due to the delay in the loop.

Fig. 5
Fig. 5

Implementation of an IIR filter. T components trim a certain number of least-significant bits from the data bus.

Fig. 6
Fig. 6

Feedback architecture for a Fabry–Perot Cavity. The electro-optic modulator (EOM) puts sidebands on the beam necessary to generate the locking signal. The FPGA algorithm TU (upper) maps the error signal to the fast VCO–AOM frequency shifting combination. The FPGA algorithm TL (lower) maps the signal to the slow PZT.

Fig. 7
Fig. 7

Bode plot of TL (lower transfer function leading to PZT). The design is a low-pass filter which dominates control below ∼100 Hz.

Fig. 8
Fig. 8

Bode plot of TU (upper transfer function leading to VCO–AOM). The peak in phase is designed to stabilize the plant through the unity gain point.

Equations (8)

Equations on this page are rendered with MathJax. Learn more.

Av=0vI(u)exp[iΦ(u)]du,
Bv=-0v exp[2iΦ(u)]du.
dΦ(v)=I(v)/v,
ϕˆ(v)=arg(Cv1-(v)Av(v)),
y(n)=i=0Na(i)u(n-i),
GC(s)=c(N)sN+c(N-1)sN-1++c(1)d(N)sN+d(N-1)sN-1++d(1),
GCGD(z)=a(0)+a(1)z-1++a(N)z-Nb(0)+b(1)z-1++b(N)z-N
y(n)=i=0Na(i)u(n-i)-i=1Nb(i)y(n-i),

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