Physical Review Letters

Ultrahigh-Resolution Spectroscopy: Photon Echoes in YAl O3 : Pr3+ and La F3 : Pr3+

R. M. Macfarlane, Robert M. Shelby, R. L. Shoemaker

Published Dec 3, 1979• 112 citations

Abstract

By using a new, delayed-heterodyne photon-echo technique, we have obtained a spectral resolving power of 1.2\ifmmode\times\else\texttimes\fi{}${10}^{11}$, measuring a 2.0-kHz linewidth (half width at half maximum) for the 6105-\AA{} $^{1}D_{2}\ensuremath{\leftrightarrow}^{3}H_{4}$ transition of YAl${\mathrm{O}}_{3}$: ${\mathrm{Pr}}^{3+}$ in an external magnetic field. This appears to be the highest resolution ever obtained in optical spectroscopy. Measurements were also made on the corresponding transition of La${\mathrm{F}}_{3}$: ${\mathrm{Pr}}^{3+}$ giving a linewidth of 5 kHz. Optical free induction decay gave incorrect results (i.e., significantly broader linewidths).

DOI: 10.1103/physrevlett.43.1726

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Physical Review Letters

Ultrahigh-Resolution Spectroscopy: Photon Echoes in YAl O3 : Pr3+ and La F3 : Pr3+

R. M. Macfarlane, Robert M. Shelby, R. L. Shoemaker

Published Dec 3, 1979• 112 citations

Publisher

Abstract

By using a new, delayed-heterodyne photon-echo technique, we have obtained a spectral resolving power of 1.2\ifmmode\times\else\texttimes\fi{}

{10}^{11}

, measuring a 2.0-kHz linewidth (half width at half maximum) for the 6105-\AA{}

^{1}D_{2}\ensuremath{\leftrightarrow}^{3}H_{4}

transition of YAl

{\mathrm{O}}_{3}

{\mathrm{Pr}}^{3+}

in an external magnetic field. This appears to be the highest resolution ever obtained in optical spectroscopy. Measurements were also made on the corresponding transition of La

{\mathrm{F}}_{3}

{\mathrm{Pr}}^{3+}

giving a linewidth of 5 kHz. Optical free induction decay gave incorrect results (i.e., significantly broader linewidths).

DOI: 10.1103/physrevlett.43.1726

Related papers

Spectroscopic and relaxation character of the P03−H43 transition in La F3 : Pr3+ measured by photon echoes

Y.C. Chen, Kophu P. Chiang, Sven R. Hartmann

The hyperfine structure and relaxation character of the terminal levels of the $^{3}P_{0}\ensuremath{-}^{3}H_{4}$ (4777 \AA{}) transition in La ${\mathrm{F}}_{3}$ : ${\mathrm{Pr}}^{3+}$ (0.03 at.%) were studied using the photon-echo technique. Using two independent nitrogen-laser pumped dye lasers we have observed modulated photon echoes for pulse separations over a \ensuremath{\sim}10-\ensuremath{\mu}sec range. In this interval our modulated photon echoes decay in a simple exponential manner by a factor of ${10}^{5}$ and yield a homogeneous linewidth of 70 kHz [full width at half maximum (FWHM)]. Fourier transformation of the echo-modulation data yields directly the nuclear level splittings and their associated linewidths in the $^{3}P_{0}$ and $^{3}H_{4}$ states. In the $^{3}P_{0}(^{3}H_{4})$ state the nuclear splittings are 0.73 and 1.12 MHz (8.48 and 16.68 MHz). The measurements for the nuclear level splittings and associated linewidths in the $^{3}H_{4}$ state are in excellent agreement with those obtained from the optical-rf double-resonance experiments of Erickson. We find that the calculated echo modulation is a sensitive function of the relative orientation of the principal axes associated with the ground-and excited-state Hamiltonians. By comparing our experimental and calculated echo-modulation patterns we are able to determine their relative orientations.The hyperfine structure and relaxation character of the terminal levels of the $^{3}P_{0}\ensuremath{-}^{3}H_{4}$ (4777 \AA{}) transition in La${\mathrm{F}}_{3}$: ${\mathrm{Pr}}^{3+}$ (0.03 at.%) were studied using the photon-echo technique. Using two independent nitrogen-laser pumped dye lasers we have observed modulated photon echoes for pulse separations over a \ensuremath{\sim}10-\ensuremath{\mu}sec range. In this interval our modulated photon echoes decay in a simple exponential manner by a factor of ${10}^{5}$ and yield a homogeneous linewidth of 70 kHz [full width at half maximum (FWHM)]. Fourier transformation of the echo-modulation data yields directly the nuclear level splittings and their associated linewidths in the $^{3}P_{0}$ and $^{3}H_{4}$ states. In the $^{3}P_{0}(^{3}H_{4})$ state the nuclear splittings are 0.73 and 1.12 MHz (8.48 and 16.68 MHz). The measurements for the nuclear level splittings and associated linewidths in the $^{3}H_{4}$ state are in excellent agreement with those obtained from the optical-rf double-resonance experiments of Erickson. We find that the calculated echo modulation is a sensitive function of the relative orientation of the principal axes associated with the ground-and excited-state Hamiltonians. By comparing our experimental and calculated echo-modulation patterns we are able to determine their relative orientations.

Physical review. B, Condensed matterJan 1, 198064 citations

Ultraslow Optical Dephasing of La F3 : Pr3+

Ralph G. DeVoe, A. Szabó, Stephen Colby Rand +1 more

Optical free-induction dephasing times as long as 16 \ensuremath{\mu}sec, corresponding to an optical homogenous linewidth of 10 kHz, have been observed for the $^{3}H_{4}\ensuremath{\leftrightarrow}^{1}D_{2}$ transition of ${\mathrm{Pr}}^{3+}$ ions in La ${\mathrm{F}}_{3}$ at 2\ifmmode^\circ\else\textdegree\fi{}K. Measurements are facilitated by a frequency-locked cw dye laser and a new form of laser frequency switching. Zeeman studies reveal a Pr-F dipole-dipole dephasing mechanism where the Pr nuclear moment is enhanced in both $^{1}D_{2}$ and $^{3}H_{4}$ .Optical free-induction dephasing times as long as 16 \ensuremath{\mu}sec, corresponding to an optical homogenous linewidth of 10 kHz, have been observed for the $^{3}H_{4}\ensuremath{\leftrightarrow}^{1}D_{2}$ transition of ${\mathrm{Pr}}^{3+}$ ions in La${\mathrm{F}}_{3}$ at 2\ifmmode^\circ\else\textdegree\fi{}K. Measurements are facilitated by a frequency-locked cw dye laser and a new form of laser frequency switching. Zeeman studies reveal a Pr-F dipole-dipole dephasing mechanism where the Pr nuclear moment is enhanced in both $^{1}D_{2}$ and $^{3}H_{4}$.

Physical Review LettersJun 4, 197970 citations

Ultrahigh-Resolution Spectroscopy: Photon Echoes in Yalo3 : Pr3+ and La F3 : Pr3+ .

R. M. Macfarlane, Robert M. Shelby, R. L. Shoemaker

Physical Review LettersJan 14, 19800 citations

Photon-echo nuclear double resonance in La F3 : Pr3+

Kophu P. Chiang, Edward A. Whittaker, Sven R. Hartmann

Using the photon-echo-nuclear-double-resonance technique, we have measured the nuclear hyperfine splittings in the excited $^{1}D_{2}$ state of La ${\mathrm{F}}_{3}$ : ${\mathrm{Pr}}^{3+}$ . Our measurements are in agreement with the results obtained by Erickson from his saturated-and-enhanced-absorption study of the $^{3}H_{4}\ensuremath{-}^{1}D_{2}$ transition in La ${\mathrm{F}}_{3}$ : ${\mathrm{Pr}}^{3+}$ .Using the photon-echo-nuclear-double-resonance technique, we have measured the nuclear hyperfine splittings in the excited $^{1}D_{2}$ state of La${\mathrm{F}}_{3}$:${\mathrm{Pr}}^{3+}$. Our measurements are in agreement with the results obtained by Erickson from his saturated-and-enhanced-absorption study of the $^{3}H_{4}\ensuremath{-}^{1}D_{2}$ transition in La${\mathrm{F}}_{3}$:${\mathrm{Pr}}^{3+}$.

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Precise Measurement of the Stark Effect with Sub-homogeneous Linewidth Resolution in Eu3+:YAIO3

Alfred Johann Meixner, C. Michael Jefferson, R. M. Macfarlane

The photon echo is often the best technique for measuring ultra narrow homogeneous linewidths of an inhomogeneously broadened optical transition for which a higher spectral resolution than the laser bandwidth is required. Homogenous linewidths on the order of one kHz have been measured for Eu3+ and Pr3+ in different host materials at liquid helium temperature from the echo intensity as a function of the delay between the two excitation pulses. These linewidths arc three orders of magnitude narrower than the long term jitter bandwidth of the laser which was used for excitation.1 Here we present a novel spectroscopic method based on the modulation of a 2-pulsc photon echo or a stimulated echo by an externally applied field, for the accurate measurement of frequency shifting perturbations with sub-homogeneous linewidth resolution. This is illustrated by the Stark effect on the 7F0→5D0 transition of Eu3+:YAIO3. The basic idea is that two coherent preparation pulses create an excited state population grating in the frequency domain of an inhomogeneously broadened line, which then gives rise to the echo in the course of the free induction decay of the coherently prepared ions. Since the photon echo can be observed for pulse separations much larger than T2, it is possible to generate frequency gratings which have a periodic spacing smaller than the homogeneous linewidth.2 In the case of a centrosymmetric crystal there are two groups of ions with equal and opposite dipole moments. An applied electric field Es shifts the ground and excited state energy levels through interaction with the electric dipole moments of these states and hence leads to a linear frequency shift, Ω=δμ⇀⋅E⇀s/ℏ, for the two sets of ions in opposite directions, where δμ⇀ is the difference between the ground and excited state dipole moments. If the electric field is applied after the first pulse, the two sets of ions accumulate equal and opposite phase shifts Φ = ± Ωt during the time interval, t. The result of the second pulse is that an excited state population grating is created in the frequency domain with a period (t + τ)-1 where t is the time interval between the pulses and τ is the duration of one pulse. Since there arc two sets of ions with opposite phase shifts, we formally get two population gratings, one with the phase Φ = + Ωt and one with the phase Φ = − Ωt. with respect to the population grating that is caused without an applied field.The photon echo is often the best technique for measuring ultra narrow homogeneous linewidths of an inhomogeneously broadened optical transition for which a higher spectral resolution than the laser bandwidth is required. Homogenous linewidths on the order of one kHz have been measured for Eu3+ and Pr3+ in different host materials at liquid helium temperature from the echo intensity as a function of the delay between the two excitation pulses. These linewidths arc three orders of magnitude narrower than the long term jitter bandwidth of the laser which was used for excitation.1 Here we present a novel spectroscopic method based on the modulation of a 2-pulsc photon echo or a stimulated echo by an externally applied field, for the accurate measurement of frequency shifting perturbations with sub-homogeneous linewidth resolution. This is illustrated by the Stark effect on the 7F0→5D0 transition of Eu3+:YAIO3. The basic idea is that two coherent preparation pulses create an excited state population grating in the frequency domain of an inhomogeneously broadened line, which then gives rise to the echo in the course of the free induction decay of the coherently prepared ions. Since the photon echo can be observed for pulse separations much larger than T2, it is possible to generate frequency gratings which have a periodic spacing smaller than the homogeneous linewidth.2 In the case of a centrosymmetric crystal there are two groups of ions with equal and opposite dipole moments. An applied electric field Es shifts the ground and excited state energy levels through interaction with the electric dipole moments of these states and hence leads to a linear frequency shift, Ω=δμ⇀⋅E⇀s/ℏ, for the two sets of ions in opposite directions, where δμ⇀ is the difference between the ground and excited state dipole moments. If the electric field is applied after the first pulse, the two sets of ions accumulate equal and opposite phase shifts Φ = ± Ωt during the time interval, t. The result of the second pulse is that an excited state population grating is created in the frequency domain with a period (t + τ)-1 where t is the time interval between the pulses and τ is the duration of one pulse. Since there arc two sets of ions with opposite phase shifts, we formally get two population gratings, one with the phase Φ = + Ωt and one with the phase Φ = − Ωt. with respect to the population grating that is caused without an applied field.

Spectral Hole-Burning and Related Spectroscopies: Science and ApplicationsJan 1, 19920 citations

Optically Detected Coherent Transients in Nuclear Hyperfine Levels

Robert M. Shelby, Constantino S. Yannoni, R. M. Macfarlane

Using optical detection, we have observed rf nutation, free-induction decay, and echoes, on the 16.70-MHz nuclear hyperfine transition of dilute ${\mathrm{Pr}}^{3+}$ in La ${\mathrm{F}}_{3}$ at 2 K. From a comparison of free-induction decay and echo decay we find that the previously observed linewidth of 200 kHz is inhomogeneous and that the homogeneous width is 19 kHz. On the basis of these measurements it is suggested that optical dephasing times for the $^{1}D_{2}\ensuremath{\leftrightarrow}^{3}H_{4}$ and $^{3}P_{0}\ensuremath{\leftrightarrow}^{3}H_{4}$ transitions are as long as \ensuremath{\sim}20 \ensuremath{\mu} sec.Using optical detection, we have observed rf nutation, free-induction decay, and echoes, on the 16.70-MHz nuclear hyperfine transition of dilute ${\mathrm{Pr}}^{3+}$ in La${\mathrm{F}}_{3}$ at 2 K. From a comparison of free-induction decay and echo decay we find that the previously observed linewidth of 200 kHz is inhomogeneous and that the homogeneous width is 19 kHz. On the basis of these measurements it is suggested that optical dephasing times for the $^{1}D_{2}\ensuremath{\leftrightarrow}^{3}H_{4}$ and $^{3}P_{0}\ensuremath{\leftrightarrow}^{3}H_{4}$ transitions are as long as \ensuremath{\sim}20 \ensuremath{\mu} sec.

Physical Review LettersDec 18, 197891 citations

By using a new, delayed-heterodyne photon-echo technique, we have obtained a spectral resolving power of 1.2\ifmmode\times\else\texttimes\fi{}

{10}^{11}

, measuring a 2.0-kHz linewidth (half width at half maximum) for the 6105-\AA{}

^{1}D_{2}\ensuremath{\leftrightarrow}^{3}H_{4}

transition of YAl

{\mathrm{O}}_{3}

{\mathrm{Pr}}^{3+}

in an external magnetic field. This appears to be the highest resolution ever obtained in optical spectroscopy. Measurements were also made on the corresponding transition of La

{\mathrm{F}}_{3}

{\mathrm{Pr}}^{3+}

giving a linewidth of 5 kHz. Optical free induction decay gave incorrect results (i.e., significantly broader linewidths).

The hyperfine structure and relaxation character of the terminal levels of the $^{3}P_{0}\ensuremath{-}^{3}H_{4}$ (4777 \AA{}) transition in La

{\mathrm{F}}_{3}

{\mathrm{Pr}}^{3+}

(0.03 at.%) were studied using the photon-echo technique. Using two independent nitrogen-laser pumped dye lasers we have observed modulated photon echoes for pulse separations over a \ensuremath{\sim}10-\ensuremath{\mu}sec range. In this interval our modulated photon echoes decay in a simple exponential manner by a factor of

{10}^{5}

and yield a homogeneous linewidth of 70 kHz [full width at half maximum (FWHM)]. Fourier transformation of the echo-modulation data yields directly the nuclear level splittings and their associated linewidths in the

^{3}P_{0}

and

^{3}H_{4}

states. In the

^{3}P_{0}(^{3}H_{4})

state the nuclear splittings are 0.73 and 1.12 MHz (8.48 and 16.68 MHz). The measurements for the nuclear level splittings and associated linewidths in the

^{3}H_{4}

state are in excellent agreement with those obtained from the optical-rf double-resonance experiments of Erickson. We find that the calculated echo modulation is a sensitive function of the relative orientation of the principal axes associated with the ground-and excited-state Hamiltonians. By comparing our experimental and calculated echo-modulation patterns we are able to determine their relative orientations.

{\mathrm{Pr}}^{3+}

ions in La

{\mathrm{F}}_{3}

at 2\ifmmode^\circ\else\textdegree\fi{}K. Measurements are facilitated by a frequency-locked cw dye laser and a new form of laser frequency switching. Zeeman studies reveal a Pr-F dipole-dipole dephasing mechanism where the Pr nuclear moment is enhanced in both

^{1}D_{2}

and

^{3}H_{4}

Using the photon-echo-nuclear-double-resonance technique, we have measured the nuclear hyperfine splittings in the excited

^{1}D_{2}

state of La

{\mathrm{F}}_{3}

{\mathrm{Pr}}^{3+}

. Our measurements are in agreement with the results obtained by Erickson from his saturated-and-enhanced-absorption study of the $^{3}H_{4}\ensuremath{-}^{1}D_{2}$ transition in La

{\mathrm{F}}_{3}

{\mathrm{Pr}}^{3+}

Using optical detection, we have observed rf nutation, free-induction decay, and echoes, on the 16.70-MHz nuclear hyperfine transition of dilute

{\mathrm{Pr}}^{3+}

in La

{\mathrm{F}}_{3}

at 2 K. From a comparison of free-induction decay and echo decay we find that the previously observed linewidth of 200 kHz is inhomogeneous and that the homogeneous width is 19 kHz. On the basis of these measurements it is suggested that optical dephasing times for the $^{1}D_{2}\ensuremath{\leftrightarrow}^{3}H_{4}$ and $^{3}P_{0}\ensuremath{\leftrightarrow}^{3}H_{4}$ transitions are as long as \ensuremath{\sim}20 \ensuremath{\mu} sec.