Abstract

We demonstrate the operation of a closed-loop fast-light cavity that allows rapid (~10 ms) measurements of the cavity mode frequency and its uncertainty. We vary the scale factor by temperature tuning the atomic density of an intracavity vapor cell. The cavity remains locked even as the system passes through the critical anomalous dispersion where a pole is observed in the scale factor. Positive and negative scale-factor enhancements as large as |S| ≈70 were obtained. To our knowledge, these are the first experiments that demonstrate a scale-factor enhancement in a closed-loop fast-light device by changing the optical path length, laying the groundwork for the improvement of cavity-based metrology instruments such as optical gyroscopes.

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References

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  1. M. S. Shahriar, G. S. Pati, R. Tripathi, V. Gopal, M. Messall, and K. Salit, “Ultrahigh enhancement in absolute and relative rotation sensing using fast and slow light,” Phys. Rev. A 75(5), 053807 (2007).
    [Crossref]
  2. D. D. Smith, H. Chang, L. Arissian, and J. C. Diels, “Dispersion enhanced laser gyroscope,” Phys. Rev. A 78(5), 053824 (2008).
    [Crossref]
  3. D. D. Smith, K. Myneni, J. A. Odutola, and J. C. Diels, “Enhanced sensitivity of a passive optical cavity by an intracavity dispersive medium,” Phys. Rev. A 80(1), 011809 (2009).
    [Crossref]
  4. H. N. Yum, M. Salit, J. Yablon, K. Salit, Y. Wang, and M. S. Shahriar, “Superluminal ring laser for hypersensitive sensing,” Opt. Express 18(17), 17658–17665 (2010).
    [Crossref] [PubMed]
  5. K. Myneni, D. D. Smith, J. A. Odutola, and C. A. Schambeau, “Tuning the scale factor and sensitivity of a passive cavity with optical pumping,” Phys. Rev. A 85(6), 063813 (2012).
    [Crossref]
  6. C. A. Christensen, A. Zavriyev, M. Bashkansky, and A. C. Beal, “Compact, fiber-based, fast-light enhanced optical gyroscope,” Proc. SPIE 8722, 87220J (2013).
    [Crossref]
  7. N. B. Phillips, I. Novikova, E. E. Mikhailov, D. Budker, and S. Rochester, “Controllable steep dispersion with gain in a four-level N-scheme with four-wave mixing,” J. Mod. Opt. 60(1), 64–72 (2013).
    [Crossref]
  8. D. D. Smith, H. Chang, K. Myneni, and A. T. Rosenberger, “Fast-light enhancement of an optical cavity by polarization mode coupling,” Phys. Rev. A 89(5), 053804 (2014).
    [Crossref]
  9. E. E. Mikhailov, J. Evans, D. Budker, S. M. Rochester, and I. Novikova, “Four-wave mixing in a ring cavity,” Opt. Eng. 53(10), 102709 (2014).
    [Crossref]
  10. J. Scheuer and S. M. Shahriar, “Lasing dynamics of super and sub luminal lasers,” Opt. Express 23(25), 32350–32366 (2015).
    [Crossref] [PubMed]
  11. D. D. Smith, H. A. Luckay, H. Chang, and K. Myneni, “Quantum-noise-limited sensitivity-enhancement of a passive optical cavity by a fast-light medium,” Phys. Rev. A 94(2), 023828 (2016).
    [Crossref]
  12. J. Yablon, Z. Zhou, M. Zhou, Y. Wang, S. Tseng, and M. S. Shahriar, “Theoretical modeling and experimental demonstration of Raman probe induced spectral dip for realizing a superluminal laser,” Opt. Express 24(24), 27444–27456 (2016).
    [Crossref] [PubMed]
  13. J. Hendrie, M. Lenzner, H. Afkhamiardakani, J. C. Diels, and L. Arissian, “Impact of resonant dispersion on the sensitivity of intracavity phase interferometry and laser gyros,” Opt. Express 24(26), 30402–30410 (2016).
    [Crossref] [PubMed]
  14. J. Wiersig, “Enhancing the sensitivity of frequency and energy splitting detection by using exceptional points: application to microcavity sensors for single-particle detection,” Phys. Rev. Lett. 112(20), 203901 (2014).
    [Crossref]
  15. J. Wiersig, “Sensors operating at exceptional points: general theory,” Phys. Rev. A 93(3), 033809 (2016).
    [Crossref]
  16. S. Sunada, “Large Sagnac frequency splitting in a ring resonator operating at an exceptional point,” Phys. Rev. A 96(3), 033842 (2017).
    [Crossref]
  17. J. Ren, H. Hodaei, G. Harari, A. U. Hassan, W. Chow, M. Soltani, D. Christodoulides, and M. Khajavikhan, “Ultrasensitive micro-scale parity-time-symmetric ring laser gyroscope,” Opt. Lett. 42(8), 1556–1559 (2017).
    [Crossref] [PubMed]
  18. H. Hodaei, A. U. Hassan, S. Wittek, H. Garcia-Gracia, R. El-Ganainy, D. N. Christodoulides, and M. Khajavikhan, “Enhanced sensitivity at higher-order exceptional points,” Nature 548(7666), 187–191 (2017).
    [Crossref] [PubMed]
  19. It is possible to implement this procedure in a closed-loop via digital processing of the data and computer-controlled feedback, but such a system would have a response time orders of magnitude slower than the analog closed-loop locking methods we present in this paper. Therefore, the advantage of our closed-loop scheme is practical, not fundamental, in nature.
  20. In PT-symmetric lasers there is another reason data is sparse in this region: although the eigenmodes of the coupled system split into two distinct frequencies, they cannot be resolved (they are indistinguishable) at sufficiently small detunings owing to their nonzero linewidths. In reference [8] we were able to obtain far more data near resonance through the use of passive coupled resonators, which are also non-Hermitian but do not require distinguishable eigenmodes to achieve the enhancement in scale factor.
  21. S. Ezekiel and S. R. Balsamo, “Passive ring resonator laser gyroscope,” Appl. Phys. Lett. 30(9), 478–480 (1977).
    [Crossref]
  22. G. A. Sanders, M. G. Prentiss, and S. Ezekiel, “Passive ring resonator method for sensitive inertial rotation measurements in geophysics and relativity,” Opt. Lett. 6(11), 569–571 (1981).
    [Crossref] [PubMed]
  23. F. Zarinetchi and S. Ezekiel, “Observation of lock-in behavior in a passive resonator gyroscope,” Opt. Lett. 11(6), 401–403 (1986).
    [Crossref] [PubMed]
  24. By “rapid” we mean in comparison to the timescale of the drift, and in comparison to previous measurements where the mode detunings had to be determined after the fact. The measurement time in our experiments was ~10 ms.
  25. H. Chang, K. Myneni, D. D. Smith, and H. R. Liaghati-Mobarhan, “High-precision, accurate optical frequency reference using a Fabry-Perót diode laser,” Rev. Sci. Instrum. 88(6), 063101 (2017).
    [Crossref] [PubMed]
  26. C. S. Edwards, H. S. Margolis, G. P. Barwood, S. N. Lea, P. Gill, G. Huang, and W. R. C. Rowley, “Absolute frequency measurement of a 1.5-mm acetylene standard by use of a combined frequency chain and femtosecond comb,” Opt. Lett. 29(6), 566–568 (2004).
    [Crossref] [PubMed]
  27. S. J. Davis, W. T. Rawlins, K. L. Galbally-Kinney, and W. J. Kessler, “Spectroscopic investigations of Rb- and Cs- rare gas systems,” Proc. SPIE 7196, 71960G (2009).
    [Crossref]
  28. The physical origin of this shift is as follows: the 87Rb, Fg = 2, D2 absorption line is a weighted average of three Doppler-broadened hyperfine resonances [11, 29]. This sum results in an asymmetric profile owing to the detunings of the various hyperfine resonances. As the Doppler widths of the individual hyperfine resonances change with temperature, the asymmetry of the overall profile is altered. So, while the individual hyperfine resonances do not shift, the weighted average does shift in frequency. The frequency shift of the absorption peak is approximately linear over the temperature range in the experiment, having a value of ≈-100 kHz/C near room temperature. For the maximum experimental temperature change of 26 C, the theory predicts a shift to lower frequencies of 2.7 MHz.
  29. K. Myneni, D. D. Smith, H. Chang, and H. A. Luckay, “Temperature sensitivity of the cavity scale factor enhancement for a Gaussian absorption resonance,” Phys. Rev. A 92(5), 053845 (2015).
    [Crossref]
  30. D. A. Steck, “Rubidium 87 D Line Data,” http://steck.us/alkalidata .
  31. D. D. Smith, K. Myneni, and H. Chang, “Dispersion enhancement in atom-cavity and coupled-cavity systems,” Proc. SPIE 8636, 86360F (2013).
    [Crossref]
  32. We also considered the possibility that the process of increasing the feedback gain might increase the noise in loop B, which would decrease the measured value of ζ in comparison with the theoretical prediction. However, inspection of Fig. 2(a) reveals that this is likely not a factor preventing observation of the enhancement in precision. The proportional gain is increased by a factor of 6.6 in this figure, yet after removing the slopes the noise that remains is roughly the same in the three sets of data. Thus, σB does not change much with temperature. This is because the noise on loop B is dominated by OPL fluctuations in the cavity, and is largely unaffected by noise introduced by the servo controller gain. Furthermore, the gain was increased more rapidly at lower temperatures, but then was held almost constant around the critical temperature, quite opposite the trend predicted for ζQNL.
  33. G. S. Pati, M. Salit, K. Salit, and M. S. Shahriar, “Demonstration of displacement–measurement–sensitivity proportional to inverse group index of intra-cavity medium in a ring resonator,” Opt. Commun. 281(19), 4931–4935 (2008).
    [Crossref]

2017 (4)

S. Sunada, “Large Sagnac frequency splitting in a ring resonator operating at an exceptional point,” Phys. Rev. A 96(3), 033842 (2017).
[Crossref]

J. Ren, H. Hodaei, G. Harari, A. U. Hassan, W. Chow, M. Soltani, D. Christodoulides, and M. Khajavikhan, “Ultrasensitive micro-scale parity-time-symmetric ring laser gyroscope,” Opt. Lett. 42(8), 1556–1559 (2017).
[Crossref] [PubMed]

H. Hodaei, A. U. Hassan, S. Wittek, H. Garcia-Gracia, R. El-Ganainy, D. N. Christodoulides, and M. Khajavikhan, “Enhanced sensitivity at higher-order exceptional points,” Nature 548(7666), 187–191 (2017).
[Crossref] [PubMed]

H. Chang, K. Myneni, D. D. Smith, and H. R. Liaghati-Mobarhan, “High-precision, accurate optical frequency reference using a Fabry-Perót diode laser,” Rev. Sci. Instrum. 88(6), 063101 (2017).
[Crossref] [PubMed]

2016 (4)

2015 (2)

J. Scheuer and S. M. Shahriar, “Lasing dynamics of super and sub luminal lasers,” Opt. Express 23(25), 32350–32366 (2015).
[Crossref] [PubMed]

K. Myneni, D. D. Smith, H. Chang, and H. A. Luckay, “Temperature sensitivity of the cavity scale factor enhancement for a Gaussian absorption resonance,” Phys. Rev. A 92(5), 053845 (2015).
[Crossref]

2014 (3)

J. Wiersig, “Enhancing the sensitivity of frequency and energy splitting detection by using exceptional points: application to microcavity sensors for single-particle detection,” Phys. Rev. Lett. 112(20), 203901 (2014).
[Crossref]

D. D. Smith, H. Chang, K. Myneni, and A. T. Rosenberger, “Fast-light enhancement of an optical cavity by polarization mode coupling,” Phys. Rev. A 89(5), 053804 (2014).
[Crossref]

E. E. Mikhailov, J. Evans, D. Budker, S. M. Rochester, and I. Novikova, “Four-wave mixing in a ring cavity,” Opt. Eng. 53(10), 102709 (2014).
[Crossref]

2013 (3)

C. A. Christensen, A. Zavriyev, M. Bashkansky, and A. C. Beal, “Compact, fiber-based, fast-light enhanced optical gyroscope,” Proc. SPIE 8722, 87220J (2013).
[Crossref]

N. B. Phillips, I. Novikova, E. E. Mikhailov, D. Budker, and S. Rochester, “Controllable steep dispersion with gain in a four-level N-scheme with four-wave mixing,” J. Mod. Opt. 60(1), 64–72 (2013).
[Crossref]

D. D. Smith, K. Myneni, and H. Chang, “Dispersion enhancement in atom-cavity and coupled-cavity systems,” Proc. SPIE 8636, 86360F (2013).
[Crossref]

2012 (1)

K. Myneni, D. D. Smith, J. A. Odutola, and C. A. Schambeau, “Tuning the scale factor and sensitivity of a passive cavity with optical pumping,” Phys. Rev. A 85(6), 063813 (2012).
[Crossref]

2010 (1)

2009 (2)

D. D. Smith, K. Myneni, J. A. Odutola, and J. C. Diels, “Enhanced sensitivity of a passive optical cavity by an intracavity dispersive medium,” Phys. Rev. A 80(1), 011809 (2009).
[Crossref]

S. J. Davis, W. T. Rawlins, K. L. Galbally-Kinney, and W. J. Kessler, “Spectroscopic investigations of Rb- and Cs- rare gas systems,” Proc. SPIE 7196, 71960G (2009).
[Crossref]

2008 (2)

G. S. Pati, M. Salit, K. Salit, and M. S. Shahriar, “Demonstration of displacement–measurement–sensitivity proportional to inverse group index of intra-cavity medium in a ring resonator,” Opt. Commun. 281(19), 4931–4935 (2008).
[Crossref]

D. D. Smith, H. Chang, L. Arissian, and J. C. Diels, “Dispersion enhanced laser gyroscope,” Phys. Rev. A 78(5), 053824 (2008).
[Crossref]

2007 (1)

M. S. Shahriar, G. S. Pati, R. Tripathi, V. Gopal, M. Messall, and K. Salit, “Ultrahigh enhancement in absolute and relative rotation sensing using fast and slow light,” Phys. Rev. A 75(5), 053807 (2007).
[Crossref]

2004 (1)

1986 (1)

1981 (1)

1977 (1)

S. Ezekiel and S. R. Balsamo, “Passive ring resonator laser gyroscope,” Appl. Phys. Lett. 30(9), 478–480 (1977).
[Crossref]

Afkhamiardakani, H.

Arissian, L.

Balsamo, S. R.

S. Ezekiel and S. R. Balsamo, “Passive ring resonator laser gyroscope,” Appl. Phys. Lett. 30(9), 478–480 (1977).
[Crossref]

Barwood, G. P.

Bashkansky, M.

C. A. Christensen, A. Zavriyev, M. Bashkansky, and A. C. Beal, “Compact, fiber-based, fast-light enhanced optical gyroscope,” Proc. SPIE 8722, 87220J (2013).
[Crossref]

Beal, A. C.

C. A. Christensen, A. Zavriyev, M. Bashkansky, and A. C. Beal, “Compact, fiber-based, fast-light enhanced optical gyroscope,” Proc. SPIE 8722, 87220J (2013).
[Crossref]

Budker, D.

E. E. Mikhailov, J. Evans, D. Budker, S. M. Rochester, and I. Novikova, “Four-wave mixing in a ring cavity,” Opt. Eng. 53(10), 102709 (2014).
[Crossref]

N. B. Phillips, I. Novikova, E. E. Mikhailov, D. Budker, and S. Rochester, “Controllable steep dispersion with gain in a four-level N-scheme with four-wave mixing,” J. Mod. Opt. 60(1), 64–72 (2013).
[Crossref]

Chang, H.

H. Chang, K. Myneni, D. D. Smith, and H. R. Liaghati-Mobarhan, “High-precision, accurate optical frequency reference using a Fabry-Perót diode laser,” Rev. Sci. Instrum. 88(6), 063101 (2017).
[Crossref] [PubMed]

D. D. Smith, H. A. Luckay, H. Chang, and K. Myneni, “Quantum-noise-limited sensitivity-enhancement of a passive optical cavity by a fast-light medium,” Phys. Rev. A 94(2), 023828 (2016).
[Crossref]

K. Myneni, D. D. Smith, H. Chang, and H. A. Luckay, “Temperature sensitivity of the cavity scale factor enhancement for a Gaussian absorption resonance,” Phys. Rev. A 92(5), 053845 (2015).
[Crossref]

D. D. Smith, H. Chang, K. Myneni, and A. T. Rosenberger, “Fast-light enhancement of an optical cavity by polarization mode coupling,” Phys. Rev. A 89(5), 053804 (2014).
[Crossref]

D. D. Smith, K. Myneni, and H. Chang, “Dispersion enhancement in atom-cavity and coupled-cavity systems,” Proc. SPIE 8636, 86360F (2013).
[Crossref]

D. D. Smith, H. Chang, L. Arissian, and J. C. Diels, “Dispersion enhanced laser gyroscope,” Phys. Rev. A 78(5), 053824 (2008).
[Crossref]

Chow, W.

Christensen, C. A.

C. A. Christensen, A. Zavriyev, M. Bashkansky, and A. C. Beal, “Compact, fiber-based, fast-light enhanced optical gyroscope,” Proc. SPIE 8722, 87220J (2013).
[Crossref]

Christodoulides, D.

Christodoulides, D. N.

H. Hodaei, A. U. Hassan, S. Wittek, H. Garcia-Gracia, R. El-Ganainy, D. N. Christodoulides, and M. Khajavikhan, “Enhanced sensitivity at higher-order exceptional points,” Nature 548(7666), 187–191 (2017).
[Crossref] [PubMed]

Davis, S. J.

S. J. Davis, W. T. Rawlins, K. L. Galbally-Kinney, and W. J. Kessler, “Spectroscopic investigations of Rb- and Cs- rare gas systems,” Proc. SPIE 7196, 71960G (2009).
[Crossref]

Diels, J. C.

J. Hendrie, M. Lenzner, H. Afkhamiardakani, J. C. Diels, and L. Arissian, “Impact of resonant dispersion on the sensitivity of intracavity phase interferometry and laser gyros,” Opt. Express 24(26), 30402–30410 (2016).
[Crossref] [PubMed]

D. D. Smith, K. Myneni, J. A. Odutola, and J. C. Diels, “Enhanced sensitivity of a passive optical cavity by an intracavity dispersive medium,” Phys. Rev. A 80(1), 011809 (2009).
[Crossref]

D. D. Smith, H. Chang, L. Arissian, and J. C. Diels, “Dispersion enhanced laser gyroscope,” Phys. Rev. A 78(5), 053824 (2008).
[Crossref]

Edwards, C. S.

El-Ganainy, R.

H. Hodaei, A. U. Hassan, S. Wittek, H. Garcia-Gracia, R. El-Ganainy, D. N. Christodoulides, and M. Khajavikhan, “Enhanced sensitivity at higher-order exceptional points,” Nature 548(7666), 187–191 (2017).
[Crossref] [PubMed]

Evans, J.

E. E. Mikhailov, J. Evans, D. Budker, S. M. Rochester, and I. Novikova, “Four-wave mixing in a ring cavity,” Opt. Eng. 53(10), 102709 (2014).
[Crossref]

Ezekiel, S.

Galbally-Kinney, K. L.

S. J. Davis, W. T. Rawlins, K. L. Galbally-Kinney, and W. J. Kessler, “Spectroscopic investigations of Rb- and Cs- rare gas systems,” Proc. SPIE 7196, 71960G (2009).
[Crossref]

Garcia-Gracia, H.

H. Hodaei, A. U. Hassan, S. Wittek, H. Garcia-Gracia, R. El-Ganainy, D. N. Christodoulides, and M. Khajavikhan, “Enhanced sensitivity at higher-order exceptional points,” Nature 548(7666), 187–191 (2017).
[Crossref] [PubMed]

Gill, P.

Gopal, V.

M. S. Shahriar, G. S. Pati, R. Tripathi, V. Gopal, M. Messall, and K. Salit, “Ultrahigh enhancement in absolute and relative rotation sensing using fast and slow light,” Phys. Rev. A 75(5), 053807 (2007).
[Crossref]

Harari, G.

Hassan, A. U.

J. Ren, H. Hodaei, G. Harari, A. U. Hassan, W. Chow, M. Soltani, D. Christodoulides, and M. Khajavikhan, “Ultrasensitive micro-scale parity-time-symmetric ring laser gyroscope,” Opt. Lett. 42(8), 1556–1559 (2017).
[Crossref] [PubMed]

H. Hodaei, A. U. Hassan, S. Wittek, H. Garcia-Gracia, R. El-Ganainy, D. N. Christodoulides, and M. Khajavikhan, “Enhanced sensitivity at higher-order exceptional points,” Nature 548(7666), 187–191 (2017).
[Crossref] [PubMed]

Hendrie, J.

Hodaei, H.

J. Ren, H. Hodaei, G. Harari, A. U. Hassan, W. Chow, M. Soltani, D. Christodoulides, and M. Khajavikhan, “Ultrasensitive micro-scale parity-time-symmetric ring laser gyroscope,” Opt. Lett. 42(8), 1556–1559 (2017).
[Crossref] [PubMed]

H. Hodaei, A. U. Hassan, S. Wittek, H. Garcia-Gracia, R. El-Ganainy, D. N. Christodoulides, and M. Khajavikhan, “Enhanced sensitivity at higher-order exceptional points,” Nature 548(7666), 187–191 (2017).
[Crossref] [PubMed]

Huang, G.

Kessler, W. J.

S. J. Davis, W. T. Rawlins, K. L. Galbally-Kinney, and W. J. Kessler, “Spectroscopic investigations of Rb- and Cs- rare gas systems,” Proc. SPIE 7196, 71960G (2009).
[Crossref]

Khajavikhan, M.

H. Hodaei, A. U. Hassan, S. Wittek, H. Garcia-Gracia, R. El-Ganainy, D. N. Christodoulides, and M. Khajavikhan, “Enhanced sensitivity at higher-order exceptional points,” Nature 548(7666), 187–191 (2017).
[Crossref] [PubMed]

J. Ren, H. Hodaei, G. Harari, A. U. Hassan, W. Chow, M. Soltani, D. Christodoulides, and M. Khajavikhan, “Ultrasensitive micro-scale parity-time-symmetric ring laser gyroscope,” Opt. Lett. 42(8), 1556–1559 (2017).
[Crossref] [PubMed]

Lea, S. N.

Lenzner, M.

Liaghati-Mobarhan, H. R.

H. Chang, K. Myneni, D. D. Smith, and H. R. Liaghati-Mobarhan, “High-precision, accurate optical frequency reference using a Fabry-Perót diode laser,” Rev. Sci. Instrum. 88(6), 063101 (2017).
[Crossref] [PubMed]

Luckay, H. A.

D. D. Smith, H. A. Luckay, H. Chang, and K. Myneni, “Quantum-noise-limited sensitivity-enhancement of a passive optical cavity by a fast-light medium,” Phys. Rev. A 94(2), 023828 (2016).
[Crossref]

K. Myneni, D. D. Smith, H. Chang, and H. A. Luckay, “Temperature sensitivity of the cavity scale factor enhancement for a Gaussian absorption resonance,” Phys. Rev. A 92(5), 053845 (2015).
[Crossref]

Margolis, H. S.

Messall, M.

M. S. Shahriar, G. S. Pati, R. Tripathi, V. Gopal, M. Messall, and K. Salit, “Ultrahigh enhancement in absolute and relative rotation sensing using fast and slow light,” Phys. Rev. A 75(5), 053807 (2007).
[Crossref]

Mikhailov, E. E.

E. E. Mikhailov, J. Evans, D. Budker, S. M. Rochester, and I. Novikova, “Four-wave mixing in a ring cavity,” Opt. Eng. 53(10), 102709 (2014).
[Crossref]

N. B. Phillips, I. Novikova, E. E. Mikhailov, D. Budker, and S. Rochester, “Controllable steep dispersion with gain in a four-level N-scheme with four-wave mixing,” J. Mod. Opt. 60(1), 64–72 (2013).
[Crossref]

Myneni, K.

H. Chang, K. Myneni, D. D. Smith, and H. R. Liaghati-Mobarhan, “High-precision, accurate optical frequency reference using a Fabry-Perót diode laser,” Rev. Sci. Instrum. 88(6), 063101 (2017).
[Crossref] [PubMed]

D. D. Smith, H. A. Luckay, H. Chang, and K. Myneni, “Quantum-noise-limited sensitivity-enhancement of a passive optical cavity by a fast-light medium,” Phys. Rev. A 94(2), 023828 (2016).
[Crossref]

K. Myneni, D. D. Smith, H. Chang, and H. A. Luckay, “Temperature sensitivity of the cavity scale factor enhancement for a Gaussian absorption resonance,” Phys. Rev. A 92(5), 053845 (2015).
[Crossref]

D. D. Smith, H. Chang, K. Myneni, and A. T. Rosenberger, “Fast-light enhancement of an optical cavity by polarization mode coupling,” Phys. Rev. A 89(5), 053804 (2014).
[Crossref]

D. D. Smith, K. Myneni, and H. Chang, “Dispersion enhancement in atom-cavity and coupled-cavity systems,” Proc. SPIE 8636, 86360F (2013).
[Crossref]

K. Myneni, D. D. Smith, J. A. Odutola, and C. A. Schambeau, “Tuning the scale factor and sensitivity of a passive cavity with optical pumping,” Phys. Rev. A 85(6), 063813 (2012).
[Crossref]

D. D. Smith, K. Myneni, J. A. Odutola, and J. C. Diels, “Enhanced sensitivity of a passive optical cavity by an intracavity dispersive medium,” Phys. Rev. A 80(1), 011809 (2009).
[Crossref]

Novikova, I.

E. E. Mikhailov, J. Evans, D. Budker, S. M. Rochester, and I. Novikova, “Four-wave mixing in a ring cavity,” Opt. Eng. 53(10), 102709 (2014).
[Crossref]

N. B. Phillips, I. Novikova, E. E. Mikhailov, D. Budker, and S. Rochester, “Controllable steep dispersion with gain in a four-level N-scheme with four-wave mixing,” J. Mod. Opt. 60(1), 64–72 (2013).
[Crossref]

Odutola, J. A.

K. Myneni, D. D. Smith, J. A. Odutola, and C. A. Schambeau, “Tuning the scale factor and sensitivity of a passive cavity with optical pumping,” Phys. Rev. A 85(6), 063813 (2012).
[Crossref]

D. D. Smith, K. Myneni, J. A. Odutola, and J. C. Diels, “Enhanced sensitivity of a passive optical cavity by an intracavity dispersive medium,” Phys. Rev. A 80(1), 011809 (2009).
[Crossref]

Pati, G. S.

G. S. Pati, M. Salit, K. Salit, and M. S. Shahriar, “Demonstration of displacement–measurement–sensitivity proportional to inverse group index of intra-cavity medium in a ring resonator,” Opt. Commun. 281(19), 4931–4935 (2008).
[Crossref]

M. S. Shahriar, G. S. Pati, R. Tripathi, V. Gopal, M. Messall, and K. Salit, “Ultrahigh enhancement in absolute and relative rotation sensing using fast and slow light,” Phys. Rev. A 75(5), 053807 (2007).
[Crossref]

Phillips, N. B.

N. B. Phillips, I. Novikova, E. E. Mikhailov, D. Budker, and S. Rochester, “Controllable steep dispersion with gain in a four-level N-scheme with four-wave mixing,” J. Mod. Opt. 60(1), 64–72 (2013).
[Crossref]

Prentiss, M. G.

Rawlins, W. T.

S. J. Davis, W. T. Rawlins, K. L. Galbally-Kinney, and W. J. Kessler, “Spectroscopic investigations of Rb- and Cs- rare gas systems,” Proc. SPIE 7196, 71960G (2009).
[Crossref]

Ren, J.

Rochester, S.

N. B. Phillips, I. Novikova, E. E. Mikhailov, D. Budker, and S. Rochester, “Controllable steep dispersion with gain in a four-level N-scheme with four-wave mixing,” J. Mod. Opt. 60(1), 64–72 (2013).
[Crossref]

Rochester, S. M.

E. E. Mikhailov, J. Evans, D. Budker, S. M. Rochester, and I. Novikova, “Four-wave mixing in a ring cavity,” Opt. Eng. 53(10), 102709 (2014).
[Crossref]

Rosenberger, A. T.

D. D. Smith, H. Chang, K. Myneni, and A. T. Rosenberger, “Fast-light enhancement of an optical cavity by polarization mode coupling,” Phys. Rev. A 89(5), 053804 (2014).
[Crossref]

Rowley, W. R. C.

Salit, K.

H. N. Yum, M. Salit, J. Yablon, K. Salit, Y. Wang, and M. S. Shahriar, “Superluminal ring laser for hypersensitive sensing,” Opt. Express 18(17), 17658–17665 (2010).
[Crossref] [PubMed]

G. S. Pati, M. Salit, K. Salit, and M. S. Shahriar, “Demonstration of displacement–measurement–sensitivity proportional to inverse group index of intra-cavity medium in a ring resonator,” Opt. Commun. 281(19), 4931–4935 (2008).
[Crossref]

M. S. Shahriar, G. S. Pati, R. Tripathi, V. Gopal, M. Messall, and K. Salit, “Ultrahigh enhancement in absolute and relative rotation sensing using fast and slow light,” Phys. Rev. A 75(5), 053807 (2007).
[Crossref]

Salit, M.

H. N. Yum, M. Salit, J. Yablon, K. Salit, Y. Wang, and M. S. Shahriar, “Superluminal ring laser for hypersensitive sensing,” Opt. Express 18(17), 17658–17665 (2010).
[Crossref] [PubMed]

G. S. Pati, M. Salit, K. Salit, and M. S. Shahriar, “Demonstration of displacement–measurement–sensitivity proportional to inverse group index of intra-cavity medium in a ring resonator,” Opt. Commun. 281(19), 4931–4935 (2008).
[Crossref]

Sanders, G. A.

Schambeau, C. A.

K. Myneni, D. D. Smith, J. A. Odutola, and C. A. Schambeau, “Tuning the scale factor and sensitivity of a passive cavity with optical pumping,” Phys. Rev. A 85(6), 063813 (2012).
[Crossref]

Scheuer, J.

Shahriar, M. S.

J. Yablon, Z. Zhou, M. Zhou, Y. Wang, S. Tseng, and M. S. Shahriar, “Theoretical modeling and experimental demonstration of Raman probe induced spectral dip for realizing a superluminal laser,” Opt. Express 24(24), 27444–27456 (2016).
[Crossref] [PubMed]

H. N. Yum, M. Salit, J. Yablon, K. Salit, Y. Wang, and M. S. Shahriar, “Superluminal ring laser for hypersensitive sensing,” Opt. Express 18(17), 17658–17665 (2010).
[Crossref] [PubMed]

G. S. Pati, M. Salit, K. Salit, and M. S. Shahriar, “Demonstration of displacement–measurement–sensitivity proportional to inverse group index of intra-cavity medium in a ring resonator,” Opt. Commun. 281(19), 4931–4935 (2008).
[Crossref]

M. S. Shahriar, G. S. Pati, R. Tripathi, V. Gopal, M. Messall, and K. Salit, “Ultrahigh enhancement in absolute and relative rotation sensing using fast and slow light,” Phys. Rev. A 75(5), 053807 (2007).
[Crossref]

Shahriar, S. M.

Smith, D. D.

H. Chang, K. Myneni, D. D. Smith, and H. R. Liaghati-Mobarhan, “High-precision, accurate optical frequency reference using a Fabry-Perót diode laser,” Rev. Sci. Instrum. 88(6), 063101 (2017).
[Crossref] [PubMed]

D. D. Smith, H. A. Luckay, H. Chang, and K. Myneni, “Quantum-noise-limited sensitivity-enhancement of a passive optical cavity by a fast-light medium,” Phys. Rev. A 94(2), 023828 (2016).
[Crossref]

K. Myneni, D. D. Smith, H. Chang, and H. A. Luckay, “Temperature sensitivity of the cavity scale factor enhancement for a Gaussian absorption resonance,” Phys. Rev. A 92(5), 053845 (2015).
[Crossref]

D. D. Smith, H. Chang, K. Myneni, and A. T. Rosenberger, “Fast-light enhancement of an optical cavity by polarization mode coupling,” Phys. Rev. A 89(5), 053804 (2014).
[Crossref]

D. D. Smith, K. Myneni, and H. Chang, “Dispersion enhancement in atom-cavity and coupled-cavity systems,” Proc. SPIE 8636, 86360F (2013).
[Crossref]

K. Myneni, D. D. Smith, J. A. Odutola, and C. A. Schambeau, “Tuning the scale factor and sensitivity of a passive cavity with optical pumping,” Phys. Rev. A 85(6), 063813 (2012).
[Crossref]

D. D. Smith, K. Myneni, J. A. Odutola, and J. C. Diels, “Enhanced sensitivity of a passive optical cavity by an intracavity dispersive medium,” Phys. Rev. A 80(1), 011809 (2009).
[Crossref]

D. D. Smith, H. Chang, L. Arissian, and J. C. Diels, “Dispersion enhanced laser gyroscope,” Phys. Rev. A 78(5), 053824 (2008).
[Crossref]

Soltani, M.

Sunada, S.

S. Sunada, “Large Sagnac frequency splitting in a ring resonator operating at an exceptional point,” Phys. Rev. A 96(3), 033842 (2017).
[Crossref]

Tripathi, R.

M. S. Shahriar, G. S. Pati, R. Tripathi, V. Gopal, M. Messall, and K. Salit, “Ultrahigh enhancement in absolute and relative rotation sensing using fast and slow light,” Phys. Rev. A 75(5), 053807 (2007).
[Crossref]

Tseng, S.

Wang, Y.

Wiersig, J.

J. Wiersig, “Sensors operating at exceptional points: general theory,” Phys. Rev. A 93(3), 033809 (2016).
[Crossref]

J. Wiersig, “Enhancing the sensitivity of frequency and energy splitting detection by using exceptional points: application to microcavity sensors for single-particle detection,” Phys. Rev. Lett. 112(20), 203901 (2014).
[Crossref]

Wittek, S.

H. Hodaei, A. U. Hassan, S. Wittek, H. Garcia-Gracia, R. El-Ganainy, D. N. Christodoulides, and M. Khajavikhan, “Enhanced sensitivity at higher-order exceptional points,” Nature 548(7666), 187–191 (2017).
[Crossref] [PubMed]

Yablon, J.

Yum, H. N.

Zarinetchi, F.

Zavriyev, A.

C. A. Christensen, A. Zavriyev, M. Bashkansky, and A. C. Beal, “Compact, fiber-based, fast-light enhanced optical gyroscope,” Proc. SPIE 8722, 87220J (2013).
[Crossref]

Zhou, M.

Zhou, Z.

Appl. Phys. Lett. (1)

S. Ezekiel and S. R. Balsamo, “Passive ring resonator laser gyroscope,” Appl. Phys. Lett. 30(9), 478–480 (1977).
[Crossref]

J. Mod. Opt. (1)

N. B. Phillips, I. Novikova, E. E. Mikhailov, D. Budker, and S. Rochester, “Controllable steep dispersion with gain in a four-level N-scheme with four-wave mixing,” J. Mod. Opt. 60(1), 64–72 (2013).
[Crossref]

Nature (1)

H. Hodaei, A. U. Hassan, S. Wittek, H. Garcia-Gracia, R. El-Ganainy, D. N. Christodoulides, and M. Khajavikhan, “Enhanced sensitivity at higher-order exceptional points,” Nature 548(7666), 187–191 (2017).
[Crossref] [PubMed]

Opt. Commun. (1)

G. S. Pati, M. Salit, K. Salit, and M. S. Shahriar, “Demonstration of displacement–measurement–sensitivity proportional to inverse group index of intra-cavity medium in a ring resonator,” Opt. Commun. 281(19), 4931–4935 (2008).
[Crossref]

Opt. Eng. (1)

E. E. Mikhailov, J. Evans, D. Budker, S. M. Rochester, and I. Novikova, “Four-wave mixing in a ring cavity,” Opt. Eng. 53(10), 102709 (2014).
[Crossref]

Opt. Express (4)

Opt. Lett. (4)

Phys. Rev. A (9)

K. Myneni, D. D. Smith, H. Chang, and H. A. Luckay, “Temperature sensitivity of the cavity scale factor enhancement for a Gaussian absorption resonance,” Phys. Rev. A 92(5), 053845 (2015).
[Crossref]

D. D. Smith, H. Chang, K. Myneni, and A. T. Rosenberger, “Fast-light enhancement of an optical cavity by polarization mode coupling,” Phys. Rev. A 89(5), 053804 (2014).
[Crossref]

M. S. Shahriar, G. S. Pati, R. Tripathi, V. Gopal, M. Messall, and K. Salit, “Ultrahigh enhancement in absolute and relative rotation sensing using fast and slow light,” Phys. Rev. A 75(5), 053807 (2007).
[Crossref]

D. D. Smith, H. Chang, L. Arissian, and J. C. Diels, “Dispersion enhanced laser gyroscope,” Phys. Rev. A 78(5), 053824 (2008).
[Crossref]

D. D. Smith, K. Myneni, J. A. Odutola, and J. C. Diels, “Enhanced sensitivity of a passive optical cavity by an intracavity dispersive medium,” Phys. Rev. A 80(1), 011809 (2009).
[Crossref]

K. Myneni, D. D. Smith, J. A. Odutola, and C. A. Schambeau, “Tuning the scale factor and sensitivity of a passive cavity with optical pumping,” Phys. Rev. A 85(6), 063813 (2012).
[Crossref]

J. Wiersig, “Sensors operating at exceptional points: general theory,” Phys. Rev. A 93(3), 033809 (2016).
[Crossref]

S. Sunada, “Large Sagnac frequency splitting in a ring resonator operating at an exceptional point,” Phys. Rev. A 96(3), 033842 (2017).
[Crossref]

D. D. Smith, H. A. Luckay, H. Chang, and K. Myneni, “Quantum-noise-limited sensitivity-enhancement of a passive optical cavity by a fast-light medium,” Phys. Rev. A 94(2), 023828 (2016).
[Crossref]

Phys. Rev. Lett. (1)

J. Wiersig, “Enhancing the sensitivity of frequency and energy splitting detection by using exceptional points: application to microcavity sensors for single-particle detection,” Phys. Rev. Lett. 112(20), 203901 (2014).
[Crossref]

Proc. SPIE (3)

C. A. Christensen, A. Zavriyev, M. Bashkansky, and A. C. Beal, “Compact, fiber-based, fast-light enhanced optical gyroscope,” Proc. SPIE 8722, 87220J (2013).
[Crossref]

S. J. Davis, W. T. Rawlins, K. L. Galbally-Kinney, and W. J. Kessler, “Spectroscopic investigations of Rb- and Cs- rare gas systems,” Proc. SPIE 7196, 71960G (2009).
[Crossref]

D. D. Smith, K. Myneni, and H. Chang, “Dispersion enhancement in atom-cavity and coupled-cavity systems,” Proc. SPIE 8636, 86360F (2013).
[Crossref]

Rev. Sci. Instrum. (1)

H. Chang, K. Myneni, D. D. Smith, and H. R. Liaghati-Mobarhan, “High-precision, accurate optical frequency reference using a Fabry-Perót diode laser,” Rev. Sci. Instrum. 88(6), 063101 (2017).
[Crossref] [PubMed]

Other (6)

We also considered the possibility that the process of increasing the feedback gain might increase the noise in loop B, which would decrease the measured value of ζ in comparison with the theoretical prediction. However, inspection of Fig. 2(a) reveals that this is likely not a factor preventing observation of the enhancement in precision. The proportional gain is increased by a factor of 6.6 in this figure, yet after removing the slopes the noise that remains is roughly the same in the three sets of data. Thus, σB does not change much with temperature. This is because the noise on loop B is dominated by OPL fluctuations in the cavity, and is largely unaffected by noise introduced by the servo controller gain. Furthermore, the gain was increased more rapidly at lower temperatures, but then was held almost constant around the critical temperature, quite opposite the trend predicted for ζQNL.

D. A. Steck, “Rubidium 87 D Line Data,” http://steck.us/alkalidata .

The physical origin of this shift is as follows: the 87Rb, Fg = 2, D2 absorption line is a weighted average of three Doppler-broadened hyperfine resonances [11, 29]. This sum results in an asymmetric profile owing to the detunings of the various hyperfine resonances. As the Doppler widths of the individual hyperfine resonances change with temperature, the asymmetry of the overall profile is altered. So, while the individual hyperfine resonances do not shift, the weighted average does shift in frequency. The frequency shift of the absorption peak is approximately linear over the temperature range in the experiment, having a value of ≈-100 kHz/C near room temperature. For the maximum experimental temperature change of 26 C, the theory predicts a shift to lower frequencies of 2.7 MHz.

By “rapid” we mean in comparison to the timescale of the drift, and in comparison to previous measurements where the mode detunings had to be determined after the fact. The measurement time in our experiments was ~10 ms.

It is possible to implement this procedure in a closed-loop via digital processing of the data and computer-controlled feedback, but such a system would have a response time orders of magnitude slower than the analog closed-loop locking methods we present in this paper. Therefore, the advantage of our closed-loop scheme is practical, not fundamental, in nature.

In PT-symmetric lasers there is another reason data is sparse in this region: although the eigenmodes of the coupled system split into two distinct frequencies, they cannot be resolved (they are indistinguishable) at sufficiently small detunings owing to their nonzero linewidths. In reference [8] we were able to obtain far more data near resonance through the use of passive coupled resonators, which are also non-Hermitian but do not require distinguishable eigenmodes to achieve the enhancement in scale factor.

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Figures (3)

Fig. 1
Fig. 1 Experimental setup. ECDL = external-cavity diode laser, ISO = isolator, HWP = half-wave plate, BS = beamsplitter, M = mirror, PZT = piezo-electric transducer, BB = beam-block. ND = neutral density filter, PD = photodetector, LIA = lock-in amplifier, PI = proportional-integral servo, CNTL = controller.
Fig. 2
Fig. 2 Representative data at three different temperatures. (a) PZT control signal at B in response to a sawtooth input at A. The data is shifted vertically for clarity. (b) Averaged data converted into FSR units through calibration. The horizontal (vertical) axis corresponds to the vertical (horizontal) axis in (a). The scale factor enhancements are obtained from the linear fits.
Fig. 3
Fig. 3 (a) Scale factor enhancement vs. temperature. The points represent measured values, whereas the solid curves were determined from the theory, and are shifted to lower temperatures by 0.84 °C. Error bars were smaller than the data symbols and are not shown, except at the most extreme values of S. A pole is observed in the data at a critical temperature of 40.8 °C. (b) Enhancement in measurement precision vs. temperature. The solid curve is the QNL prediction at high signal-to-noise. The data is adjusted (open circles) to take into account the reversed input-output arrangement.

Equations (1)

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ζ=| S |/ε,

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