Periodic Reporting for period 1 - UltraStabLaserViaSHB (Ultra Frequency-Stable Laser via Spectral Hole Burning in Rare-earth Ion Doped Crystals)
Reporting period: 2022-10-01 to 2024-09-30
Summary of the context and overall objectives of the project
With the redefinition of the Système International d’unités (SI) base units in 2019, the unit of the second (s) sees itself in a position of significance, where now, with the exception of the mole, all other SI base units are linked to the second [1]. Currently, the second is defined by the microwave radiation at the frequency corresponding to the transition between hyperfine levels of the ground state of the cesium atom. With the first such atomic clocks produced in the 1950s, adoption of the cesium standard second has led to the development of atomic clocks which can measure the second with a relative uncertainty on the order of 1 part per 10 to the power 16.
Meanwhile, clocks based on cavity-stabilized lasers probing atomic or ionic optical transition frequencies have come to surpass the accuracy in cesium atomic clocks by more than an order of magnitude [2]. The technical superiority of frequency measurement at optical transitions have effected a push towards a future redefinition of the SI second to be based on optical clocks [3]. While optical clocks have come to outperform cesium clocks, they still have not achieved their theoretical performance level set by the quantum projection noise limit. The current limiting technical noise source which diminishes their performance is the frequency fluctuations of the cavity-stabilized probe lasers [4], that is, a laser referenced to the resonant frequency of an optical cavity composed of two partially reflective mirrors held a precise distance apart. In such a system, the stability of the distance between the mirrors’ surfaces determines the frequency stability of the controlled laser.
This brings us to the core subject of this research project, the development of a novel type of ultra-stable laser. For decades, ultra-stable lasers have been realized by stabilization to an optical cavity. This mature technology has approached its fundamental physical performance limit, set by thermal noise in the cavity mirrors, to a fractional frequency instability of about 1 part in 10 to the power 16 over a 1 second measurement time [5][6]. While large field cavities cooled to cryogenic temperatures have pushed this limit to several parts in 10 to the power 17, this falls short of the stability requirements of order 1 part in 10 to the power 18 needed to realize the quantum project noise limited performance of optical lattice clocks.
This project explored the performance limits of a novel frequency stabilization technique via Spectral-Hole Burning (SHB). Briefly, the process of SHB involves the use of a relatively high-power pump laser to ‘burn’ or bleach a narrow transmission line at the particular wavelength(s) of the pump laser. The result is a spectral feature which is transparent to a select laser frequency in an otherwise opaque material. After pumping, we can frequency stabilize a probe laser to this spectral line. Early first experiments in SHB laser stabilization were carried out at sample temperatures of about 4 kelvin to preserve the longevity of the spectral holes. The system selected in these experiments, europium 3+ doped into an yttrium orthosilicate crystal matrix (Eu:YSO), is chosen for its desirable spectroscopic properties. These early results identified two key difficulties in achieving a performant SHB stabilized laser [7][8]:
The degradation of spectral-holes under high power probing conditions limits probe beam power. This reduces available optical signal and thus accentuates detection noise and shot-noise.
Temperature fluctuations in the sample crystal cryostat produced thermally induced spectral-hole line shifts translating to frequency fluctuations.
In short, this project addressed these challenges by:
implementing and characterizing a multi-spectral hole burning and probing scheme to reduce detection noise
Installation of a dilution refrigerator for operation at sub-kelvin temperatures to reduce spectral-hole temperature sensitivity
The project represented, in part, the first operation and characterization of spectral-holes at sub-kelvin temperatures, and the results will guide, not only future SHB laser stabilization research, but all sub-kelvin SHB experiments.
[1] Bureau international des poids et mesures, Le Système international d’unités, 9e édition (Paris, 2019)
[2] T. L. Nicholson, et al., Nature Communications 6, 6896 (2015).
[3] F. Riehle, Comptes Rendus Physique 16, 506-515 (2015).
[4] T. L. Nicholson, et al., Phys. Rev. Lett. 109, 230801 (2012).
[5] K. Numata, et al., Phys. Rev. Lett. 93, 250602 (2004).
[6] M. Notcutt, et al., Opt. Lett. 30, 1815–1817 (2005).
[7] M. J. Thorpe, et al., Nature Photon. pp. 688–693 (2011).
[8] N. Galland, et al., Opt. Lett. 45, 1930–1933 (2020)
Meanwhile, clocks based on cavity-stabilized lasers probing atomic or ionic optical transition frequencies have come to surpass the accuracy in cesium atomic clocks by more than an order of magnitude [2]. The technical superiority of frequency measurement at optical transitions have effected a push towards a future redefinition of the SI second to be based on optical clocks [3]. While optical clocks have come to outperform cesium clocks, they still have not achieved their theoretical performance level set by the quantum projection noise limit. The current limiting technical noise source which diminishes their performance is the frequency fluctuations of the cavity-stabilized probe lasers [4], that is, a laser referenced to the resonant frequency of an optical cavity composed of two partially reflective mirrors held a precise distance apart. In such a system, the stability of the distance between the mirrors’ surfaces determines the frequency stability of the controlled laser.
This brings us to the core subject of this research project, the development of a novel type of ultra-stable laser. For decades, ultra-stable lasers have been realized by stabilization to an optical cavity. This mature technology has approached its fundamental physical performance limit, set by thermal noise in the cavity mirrors, to a fractional frequency instability of about 1 part in 10 to the power 16 over a 1 second measurement time [5][6]. While large field cavities cooled to cryogenic temperatures have pushed this limit to several parts in 10 to the power 17, this falls short of the stability requirements of order 1 part in 10 to the power 18 needed to realize the quantum project noise limited performance of optical lattice clocks.
This project explored the performance limits of a novel frequency stabilization technique via Spectral-Hole Burning (SHB). Briefly, the process of SHB involves the use of a relatively high-power pump laser to ‘burn’ or bleach a narrow transmission line at the particular wavelength(s) of the pump laser. The result is a spectral feature which is transparent to a select laser frequency in an otherwise opaque material. After pumping, we can frequency stabilize a probe laser to this spectral line. Early first experiments in SHB laser stabilization were carried out at sample temperatures of about 4 kelvin to preserve the longevity of the spectral holes. The system selected in these experiments, europium 3+ doped into an yttrium orthosilicate crystal matrix (Eu:YSO), is chosen for its desirable spectroscopic properties. These early results identified two key difficulties in achieving a performant SHB stabilized laser [7][8]:
The degradation of spectral-holes under high power probing conditions limits probe beam power. This reduces available optical signal and thus accentuates detection noise and shot-noise.
Temperature fluctuations in the sample crystal cryostat produced thermally induced spectral-hole line shifts translating to frequency fluctuations.
In short, this project addressed these challenges by:
implementing and characterizing a multi-spectral hole burning and probing scheme to reduce detection noise
Installation of a dilution refrigerator for operation at sub-kelvin temperatures to reduce spectral-hole temperature sensitivity
The project represented, in part, the first operation and characterization of spectral-holes at sub-kelvin temperatures, and the results will guide, not only future SHB laser stabilization research, but all sub-kelvin SHB experiments.
[1] Bureau international des poids et mesures, Le Système international d’unités, 9e édition (Paris, 2019)
[2] T. L. Nicholson, et al., Nature Communications 6, 6896 (2015).
[3] F. Riehle, Comptes Rendus Physique 16, 506-515 (2015).
[4] T. L. Nicholson, et al., Phys. Rev. Lett. 109, 230801 (2012).
[5] K. Numata, et al., Phys. Rev. Lett. 93, 250602 (2004).
[6] M. Notcutt, et al., Opt. Lett. 30, 1815–1817 (2005).
[7] M. J. Thorpe, et al., Nature Photon. pp. 688–693 (2011).
[8] N. Galland, et al., Opt. Lett. 45, 1930–1933 (2020)
Work performed from the beginning of the project to the end of the period covered by the report and main results achieved so far
The work performed in this project was targeted to address the two main challenges (described in the above Context and Overview) that were uncovered in early work with laser stabilization via spectral-hole burning (SHB). The result of this project were three significant breakthroughs in the field of SHB:
I) The novel development and characterization of a simultaneous multi-spectral-hole burning and subsequent simultaneous multi-hole probing scheme.
II) The first ever SHB experiment performed at sub-kelvin temperatures, and the subsequent characterization of spectral-hole properties and temperature-dependent line shifts in this regime.
III) The first ever estimates of fundamental frequency stability limits of spectral-holes, namely the calculation of thermal-noise in spectral-holes.
Briefly, the work involved on these subjects are described here:
I) As mentioned in the Context and Overview, performant SHB laser stabilization see difficulties due to the requirement of low-laser-power (~10 nW) to avoid “over-burning” (spectral broadening due to continuous excitation of neighboring ions) from the probe beam. The solution explored in this project involved the use of an Ettus X310 Software Defined Radio (SDR) to produce a multi-tonal RF electrical signal which could then drive an AOM to produce a laser beam composed of multiple frequency components to burn multiple spectral holes. Frequency shifting the probe beam allows us to probe the multiple spectral holes simultaneously, while the SDR can receive the resulting multi-modal signal from a photodetector, separate the frequency components and synthesize a laser control signal using the average of multiple spectral holes. Keeping the per-hole-power the same in the probe laser, this effectively increased the signal to noise ratio, reducing detection noise. The success of this work prompted us to publish our results where we detail our optimization of our platform, produce noise characterization with appropriate calculation, and demonstrate through measurement the successful reduction of quantum detection noise using this novel multi-mode heterodyne technique [9].
II) As mentioned in the Context and Overview, early SHB laser stabilization experiments found that they are limited by temperature fluctuations coupling to temperature-dependent line shifts due to phonon scattering, where the shift is a function of temperature to the fourth power. The motivation is a reduction of temperature sensitivity, reducing cryostat temperature noise well below the quantum detection limit. This work involved the installation of a Helium-3/Hemium-4 dilution refrigerator to achieve operating temperatures in a range from 0.1 to 1 kelvin. Here we were able to measure the spectroscopic properties of SHB at sub-kelvin temperatures for the first time, demonstrating an optimization of pump energies (burning power and duration) at these new temperatures, as well as the characterization of spectral hole linewidths in a new physical regime [10]. Furthermore, to characterize the spectral-hole temperature sensitivity at ultra-low temperatures, we measured the thermal induced spectral line shifts of spectral-holes, finding the expected phonon-scatter model driven T to the fourth power dependence at the spectroscopic site 2, but discovering a deviation from this model at site 1, revealing a coveted point of temperature insensitivity and suggestion new physics in this system [11].
III) To understand the fundamental limits to frequency stability in spectral-holes, we developed a set of thermal-noise models for the sample, articulating the fundamental physical limits fixed by thermodynamics in the system. The results constitute, to our knowledge, the first such modelization in spectral hole systems and are being communicated via an article currently in publication [12]. This work, in conjunction with past SHB experimental measurements and the other characterizations realised in this project, permitted the calculation of thermo-dynamically driven fluctuations of spectral-hole frequency. To realize the calculation of Brownian thermal noise, knowledge of the mechanical quality factor of the crystal system was necessary. This was realized through international collaboration with the Institute of Semiconductor Technology (Institut für Halbleitertechnik, Technische Universität Braunschweig) in the development of a testbed for the determination of mechanical loss angle through ring-down measurement. This resulted in preparation of a manuscript presenting the first Q-factor measurements in YSO [13] and helped found a working interdisciplinary collaboration between these teams.
[9] X. Lin, M. T. Hartman, S. Zhang, S. Seidelin, B. Fang, and Y. Le Coq, "Multi-mode heterodyne laser interferometry realized via software defined radio," Opt. Express 31, 38475-38493 (2023).
[10] X. Lin, M. T. Hartman, P. Goldner, B. Fang, Y. Le Coq, and S. Seidelin, “Homogeneous Linewidth Behaviour of Narrow Optical Emitters at Sub-kelvin Temperatures”: MANUSCRIPT IN PREPARATION
[11] X. Lin, M. T. Hartman, B. Pointard, R. Le Targat, P. Goldner, S. Seidelin, B. Fang, and Y. Le Coq, “Anomalous Subkelvin Thermal Frequency Shifts of Ultranarrow Linewidth Solid State Emitters,” Phys. Rev. Lett. 133, 183803
[12] M. T. Hartman, N. Wagner, S. Seidelin, and B. Fang, “Thermal-noise Limits to the Frequency Stability of Burned Spectral Holes,” : MANUSCRIPT IN PREPARATION
[13] Nico Wagner, Johannes Dickmann, Bess Fang, Michael T. Hartman, Stefanie Kroker, “Temperature-dependent mechanical losses of Eu3+:Y2SiO5 for spectral hole burning laser stabilization”: MANUSCRIPT IN PREPARATION
I) The novel development and characterization of a simultaneous multi-spectral-hole burning and subsequent simultaneous multi-hole probing scheme.
II) The first ever SHB experiment performed at sub-kelvin temperatures, and the subsequent characterization of spectral-hole properties and temperature-dependent line shifts in this regime.
III) The first ever estimates of fundamental frequency stability limits of spectral-holes, namely the calculation of thermal-noise in spectral-holes.
Briefly, the work involved on these subjects are described here:
I) As mentioned in the Context and Overview, performant SHB laser stabilization see difficulties due to the requirement of low-laser-power (~10 nW) to avoid “over-burning” (spectral broadening due to continuous excitation of neighboring ions) from the probe beam. The solution explored in this project involved the use of an Ettus X310 Software Defined Radio (SDR) to produce a multi-tonal RF electrical signal which could then drive an AOM to produce a laser beam composed of multiple frequency components to burn multiple spectral holes. Frequency shifting the probe beam allows us to probe the multiple spectral holes simultaneously, while the SDR can receive the resulting multi-modal signal from a photodetector, separate the frequency components and synthesize a laser control signal using the average of multiple spectral holes. Keeping the per-hole-power the same in the probe laser, this effectively increased the signal to noise ratio, reducing detection noise. The success of this work prompted us to publish our results where we detail our optimization of our platform, produce noise characterization with appropriate calculation, and demonstrate through measurement the successful reduction of quantum detection noise using this novel multi-mode heterodyne technique [9].
II) As mentioned in the Context and Overview, early SHB laser stabilization experiments found that they are limited by temperature fluctuations coupling to temperature-dependent line shifts due to phonon scattering, where the shift is a function of temperature to the fourth power. The motivation is a reduction of temperature sensitivity, reducing cryostat temperature noise well below the quantum detection limit. This work involved the installation of a Helium-3/Hemium-4 dilution refrigerator to achieve operating temperatures in a range from 0.1 to 1 kelvin. Here we were able to measure the spectroscopic properties of SHB at sub-kelvin temperatures for the first time, demonstrating an optimization of pump energies (burning power and duration) at these new temperatures, as well as the characterization of spectral hole linewidths in a new physical regime [10]. Furthermore, to characterize the spectral-hole temperature sensitivity at ultra-low temperatures, we measured the thermal induced spectral line shifts of spectral-holes, finding the expected phonon-scatter model driven T to the fourth power dependence at the spectroscopic site 2, but discovering a deviation from this model at site 1, revealing a coveted point of temperature insensitivity and suggestion new physics in this system [11].
III) To understand the fundamental limits to frequency stability in spectral-holes, we developed a set of thermal-noise models for the sample, articulating the fundamental physical limits fixed by thermodynamics in the system. The results constitute, to our knowledge, the first such modelization in spectral hole systems and are being communicated via an article currently in publication [12]. This work, in conjunction with past SHB experimental measurements and the other characterizations realised in this project, permitted the calculation of thermo-dynamically driven fluctuations of spectral-hole frequency. To realize the calculation of Brownian thermal noise, knowledge of the mechanical quality factor of the crystal system was necessary. This was realized through international collaboration with the Institute of Semiconductor Technology (Institut für Halbleitertechnik, Technische Universität Braunschweig) in the development of a testbed for the determination of mechanical loss angle through ring-down measurement. This resulted in preparation of a manuscript presenting the first Q-factor measurements in YSO [13] and helped found a working interdisciplinary collaboration between these teams.
[9] X. Lin, M. T. Hartman, S. Zhang, S. Seidelin, B. Fang, and Y. Le Coq, "Multi-mode heterodyne laser interferometry realized via software defined radio," Opt. Express 31, 38475-38493 (2023).
[10] X. Lin, M. T. Hartman, P. Goldner, B. Fang, Y. Le Coq, and S. Seidelin, “Homogeneous Linewidth Behaviour of Narrow Optical Emitters at Sub-kelvin Temperatures”: MANUSCRIPT IN PREPARATION
[11] X. Lin, M. T. Hartman, B. Pointard, R. Le Targat, P. Goldner, S. Seidelin, B. Fang, and Y. Le Coq, “Anomalous Subkelvin Thermal Frequency Shifts of Ultranarrow Linewidth Solid State Emitters,” Phys. Rev. Lett. 133, 183803
[12] M. T. Hartman, N. Wagner, S. Seidelin, and B. Fang, “Thermal-noise Limits to the Frequency Stability of Burned Spectral Holes,” : MANUSCRIPT IN PREPARATION
[13] Nico Wagner, Johannes Dickmann, Bess Fang, Michael T. Hartman, Stefanie Kroker, “Temperature-dependent mechanical losses of Eu3+:Y2SiO5 for spectral hole burning laser stabilization”: MANUSCRIPT IN PREPARATION
Progress beyond the state of the art and expected potential impact (including the socio-economic impact and the wider societal implications of the project so far)
The main scientific results of this project were three fold, each with benefits extending beyond the SHB experiment at SYRTE:
i) The development characterization of a multi-mode heterodyne interferometric scheme provides a model for the application of a commercial technology (a software defined radio) towards cutting edge scientific research. This technique will be applicable not only to the SHB SYRTE experiment nor only SHB experiments in general, but to all laser interferometry experiments seeking to leverage multi-mode heterodyne detection. The results were published in an open-access peer reviewed journal to benefit the scientific community at large [9].
ii) The first ever sub-kelvin spectral hole burning experimental results will produce a reference for all SHB experiments, present and future. The results are, at its core, the definition of ground-breaking, and have resulted in two journal articles, one published in a peer-reviewed open access letter [11] and the other forms a manuscript currently in preparation [10]. Beyond the immediate publications, the results motivate the further investigation of material properties at sub K temperature in order to shed light on the physical mechanism that causes the deviation from the known theoretical model. This direction is currently pursued by the host group, in collaboration with material experts at Institut de Recherche de Chimie Paris and cryogenics experts at Institut Néel. An open question raised by this investigation was the discovery of a photo-induced, non-resonant luminescence phenomenon, which results in degradation of the detection noise. Whereas a strategy is found for its mitigation under current test cases, a more comprehensive investigation is needed for a better understanding of the physics behind this emission. Being the first group observing the phenomenon, the host will further study this phenomenon, with the support from other players in the rare-earth community.
iii) These measurements of spectral-hole properties, along with past experimental data, provided the characterizations needed for the estimation of thermal-noise in spectral-hole systems. This motivated our development of thermal-noise models for spectral holes. Previously not clearly defined, this work establishes the fundamental physical limits of spectral-hole frequency stability as a function of experimental and material properties. Currently in preparation for publication [12], these results will guide the planning and design as a foundation of future spectral-hole experiments. Furthermore, the need for a measurement of mechanical resonance quality factor in the crystalline host nurtured the development of a collaboration between the SHB project host institution (SYRTE, Observatoire de Paris; Paris, Fance) and an experimental materials group in Braunschweig (Technische Universität Braunschweig; Braunschweig, Germany). This collaboration helped the development of both experimental groups and provided a foundation for future collaboration between these disciplines.
i) The development characterization of a multi-mode heterodyne interferometric scheme provides a model for the application of a commercial technology (a software defined radio) towards cutting edge scientific research. This technique will be applicable not only to the SHB SYRTE experiment nor only SHB experiments in general, but to all laser interferometry experiments seeking to leverage multi-mode heterodyne detection. The results were published in an open-access peer reviewed journal to benefit the scientific community at large [9].
ii) The first ever sub-kelvin spectral hole burning experimental results will produce a reference for all SHB experiments, present and future. The results are, at its core, the definition of ground-breaking, and have resulted in two journal articles, one published in a peer-reviewed open access letter [11] and the other forms a manuscript currently in preparation [10]. Beyond the immediate publications, the results motivate the further investigation of material properties at sub K temperature in order to shed light on the physical mechanism that causes the deviation from the known theoretical model. This direction is currently pursued by the host group, in collaboration with material experts at Institut de Recherche de Chimie Paris and cryogenics experts at Institut Néel. An open question raised by this investigation was the discovery of a photo-induced, non-resonant luminescence phenomenon, which results in degradation of the detection noise. Whereas a strategy is found for its mitigation under current test cases, a more comprehensive investigation is needed for a better understanding of the physics behind this emission. Being the first group observing the phenomenon, the host will further study this phenomenon, with the support from other players in the rare-earth community.
iii) These measurements of spectral-hole properties, along with past experimental data, provided the characterizations needed for the estimation of thermal-noise in spectral-hole systems. This motivated our development of thermal-noise models for spectral holes. Previously not clearly defined, this work establishes the fundamental physical limits of spectral-hole frequency stability as a function of experimental and material properties. Currently in preparation for publication [12], these results will guide the planning and design as a foundation of future spectral-hole experiments. Furthermore, the need for a measurement of mechanical resonance quality factor in the crystalline host nurtured the development of a collaboration between the SHB project host institution (SYRTE, Observatoire de Paris; Paris, Fance) and an experimental materials group in Braunschweig (Technische Universität Braunschweig; Braunschweig, Germany). This collaboration helped the development of both experimental groups and provided a foundation for future collaboration between these disciplines.