A microphotonic astrocomb

Transcription

1 SUPPLEMENTARY INFORMATION Letters In the format provided by the authors and unedited. A microphotonic astrocomb Ewelina Obrzud 1,2, Monica Rainer 3,8, Avet Harutyunyan 4, Miles H. Anderson 5, Junqiu Liu 5, Michael Geiselmann 5,6, Bruno Chazelas 2, Stefan Kundermann 1, Steve Lecomte 1, Massimo Cecconi 4, Adriano Ghedina 4, Emilio Molinari 4,7, Francesco Pepe 2, François Wildi 2, François Bouchy 2, Tobias J. Kippenberg 5 and Tobias Herr 1 * 1 Swiss Centre for Electronics and Microtechnology (CSEM), Time and Frequency Sector, Neuchâtel, Switzerland. 2 University of Geneva, Department of Astronomy & Geneva Observatory/PlanetS, Versoix, Switzerland. 3 National Institute of Astrophysics (INAF), Astronomical Observatory of Brera, Milano, Italy. 4 National Institute of Astrophysics (INAF), Fundación Galileo Galilei, Breña Baja, Santa Cruz de Tenerife, Spain. 5 Swiss Federal Institute of Technology (EPFL), Photonics and Quantum Measurements, SB IPHYS LPQM, Lausanne, Switzerland. 6 Ligentec, EPFL Innovation Park, Bâtiment C, Lausanne, Switzerland. 7 National Institute of Astrophysics (INAF), Osservatorio Astronomico di Cagliari, Selargius, Italy. 8 Present address: National Institute of Astrophysics (INAF), Arcetri Astrophysical Observatory, Florence, Italy. * tobias.herr@csem.ch Nature Photonics

2 A microphotonic Astrocomb - Supplementary Information Ewelina Obrzud 1,2, Monica Rainer 3, Avet Harutyunyan 4, Miles H. Anderson 5, Junqui Liu 5, Michael Geiselmann 5,6, Bruno Chazelas 2, Stefan Kundermann 1, Steve Lecomte 1 Massimo Cecconi 4, Adriano Ghedina 4, Emilio Molinari 4,7, Francesco Pepe 2, François Wildi 2, François Bouchy 2, Tobias J. Kippenberg 5 & Tobias Herr 1 1 Swiss Centre for Electronics and Microtechnology (CSEM), Time and Frequency Sector, Rue de l Observatoire 58, 2002 Neuchâtel, Switzerland 2 University of Geneva, Department of Astronomy & Geneva Observatory/PlanetS, Chemin des Maillettes 51, 1290 Versoix, Switzerland 3 National Institute of Astrophysics (INAF), Astronomical Observatory of Brera, Via Brera 28, Milano, Italy 4 National Institute of Astrophysics (INAF), Fundación Galileo Galilei, Rambla José Ana Fernández Pérez 7, Breña Baja, Santa Cruz de Tenerife, Spain 5 Swiss Federal Institute of Technology (EPFL), Photonics and Quantum Measurements, SB IPHYS LPQM1, PH D3, Station 3, 1015 Lausanne, Switzerland 6 Ligentec, EPFL Innovation Park, Bâtiment C, 1015 Lausanne, Switzerland 7 National Institute of Astrophysics (INAF), Osservatorio Astronomico di Cagliari, Via della Scienza Selargius (CA), Italy 1 Stability of the microphotonic astrocomb General remarks on the stability of frequency combs. The current definition of frequency (and therefore wavelength) is based on the ground state hyper-fine transition frequency in caesium- 133 (Cs) at 9 GHz. Frequency combs permit synthesis of optical lines whose frequencies are directly referenced to the absolute Cs-standard, hence providing the unique and unprecedented opportunity for absolute spectrometer calibration. The optical frequencies ν n of the comb lines are fully described by the relation ν n = n f rep + f 0, where the pulse repetition rate (i.e. the comb line spacing) f rep and the offset frequency f 0 (n is an integer). By linking both f rep and f 0 to the Cs-based frequency standard also the optical frequencies ν n are referenced to the Cs-standard with the same relative stability and accuracy. As Cs-primary clocks are extremely complex and costly systems and limited to major national metrology laboratories, frequency combs are typically not directly referenced to the Cs-standard, but rather to a stable local radio-frequency (RF) oscillator such as a compact atomic rubidium-clock (RB-clock) as in the present work. While these local oscillators provide sufficient short-term stability (as will be detailed below), they will lose accuracy over time due to drift and ageing effects. For the Rb-clock used here the relative effect of ageing is approximately per year equating to a radial velocity error of 15 cm/s per year. This growing inaccuracy could impede the detection of small, Earth-like planets and would pose a severe limitation to cosmological observations. In order to nevertheless provide long term accuracy 1

3 the local RF oscillators can be disciplined to the absolute Cs-standard on medium time scales (minutes to hours) limiting their inaccuracy. In the present case the Rb-clock is disciplined to the Cs-standard via the global-position system (GPS), resulting in an absolute accuracy of on any long time scale corresponding to sub-mm/s radial velocities. On short-time scales frequency combs will be fundamentally limited by the stability of the local oscillator frequency standard. In addition, laser frequency noise in f rep and f 0 will further reduce the stability on short time scales. In the following, the long- and short-term stability of the present astrocomb system is discussed. Here, we loosely define long- and short-term as time scales that are significantly longer or comparable to the exposure time required for achieving a single spectrometer calibration (10 s in the present case), respectively. Long-term stability of the microphotonic astrocomb. In the present case of the microphotonic astrocomb the comb s line spacing frep astro is given by the soliton pulse repetition rate. Owing to the sub-harmonic pulsed driving scheme, the soliton s repetition rate is directly determined by the exact double of the microwave frequency driving the electro-optic modulators. As the microwave source is directly referenced to the GPS-disciplined Rb-clock, frep astro acquires the long term accuracy and stability of the Cs-based frequency standard. The remaining parameter is the astrocomb s offset frequency f 0 which is conveniently controlled by the frequency of the CW laser (cf. Fig. 1 in the main text), which already constitutes one of the astrocomb s lines. As measuring f 0 for a highrepetition rate astrocomb is challenging, we take a different approach and lock the offset frequency f0 astro of the astrocomb, by offset-locking the CW laser to the nearest comb line of a conventional self-referenced low-repetition rate (100 MHz) mode-locked laser (MLL). By referencing f 0 and f rep of the MLL as well as the offset-lock frequency to the GPS-disciplined Rb-clock, the astrocomb s offset f0 astro acquires the long term accuracy and stability of the Cs-based frequency standard. In summary, on long time scales, the microphotonic astrocomb inherits the per definition absolute accuracy and long-term stability of the Cs-based time and frequency standard. Short-term stability of the microphotonic astrocomb. A number of technical components limit the frequency stability of the microphotonic astrocomb on short time scales. The impact of these individual technical components is illustrated in Figure 1a in terms of their effect on the actual frequency stability of the astrocomb s lines. In order to derive the data in Figure 1a, the Allan deviation of the relevant frequencies has been measured and multiplied with the respective relevant carrier frequency (more detail will be provided below). Importantly, Figure 1 shows that the microphotonic astrocomb provides sufficient short-term stability to support spectrometer calibration on the level of 1 cm/s for exposure times of 1 s and longer (in the present work we used exposure times of 10 s). In the following the components limiting the short-term stability and the method of determining these limits will be discussed: Rb-clock: On short time scales the stability and hence the calibration precision cannot be better than the RF standard to which the comb is referenced. This implies that the Rb- 2

4 clock poses a fundamental limitation to the stability on short time scales. Its impact on the astrocomb s short-term stability can be found by multiplying its relative stability with the optical frequency of the astrocomb ( 193 THz). The result is shown in Figure 1a (white line Rb clock ). Microwave-synthesizer: The astrocomb s line spacing, i.e. the soliton s repetition rate is defined by and tightly locked to the microwave synthesizer (within a feedback bandwidth corresponding to the microresonator s resonance width). This is illustrated in Figure 1b, which shows the matching phase noises of the microwave synthesizer and of the soliton s repetition rate (measured in the wing of the soliton spectrum at 1515 nm in a 1 nm wide span). In particular, no excess noise resulting from the erbium-doped fibre amplifier (EDFA) is apparent at the relevant frequencies. While the microwave synthesizer defining the astrocomb s line spacing frep astro is directly referenced to the Rb-clock, it will add a certain amount of excess noise when generating the microwave frequency driving the modulators. Any additional instability in the synthesizer will lead to an additional breathing of the comb lines around the frequency defined by the CW laser. In order to determine the impact of this effect, the relative excess noise is measured (at 24 MHz) and multiplied with the spectral distance between CW laser and far-out wing (15 THz). The corresponding result in Figure 1a (blue line MW synthesizer ) shows that the stability of the microwave synthesizer is not limiting the astrocomb s short-term performance and will indeed be compatible with much broader spectra in the future. Locking of the CW laser to the MLL: Even for a perfectly stable MLL comb (which is not the case as will be discussed below) the instability in locking the CW laser to the MLL will directly translate to instability in the astrocomb s offset f0 astro. The lock is implemented as an offset lock, locking the CW laser at a 10 MHz offset to one of the MLL s lines. In order to quantify the resulting noise on f0 astro the relative stability of the offset lock is measured (out-of-loop) and multiplied with the offset frequency. The resulting contribution to the instability of f0 astro is shown in Figure 1a (blue line CW laser lock ). RF-to-optical link via the MLL: The stability of the the astrocomb s offset frequency f0 astro is indeed limited by the instability of the MLL s f rep. The measured (out-of-loop) relative instability of f rep is multiplied with the optical frequency of the astrocomb ( 193 THz) in order to calculate the resulting instability of the MLL line to which the CW laser is locked. Due to the large multiplication factor, the resulting instability in the astrocomb s offset f0 astro is significant as shown in Figure 1a (black line MLL f rep lock ). Exposure times of 1 s or longer are required if a precision of 1 cm/s is to be reached. Note that the instability related to the MLL s f 0 lock is negligible but also shown for completeness in Figure 1a (black line MLL f 0 lock ). In summary, all contributions limiting the astrocomb s stability are smaller than what is required to support a calibration precision of < 1 cm/s already after 1 s of averaging (i.e. exposure 3

5 time). 2 The Giano-B spectromter GIANO-B is a near-infrared high resolution spectrometer mounted at the Telescopio Nazionale Galileo (TNG). GIANO-B provides cross-dispersed echelle slit spectroscopy at a resolution of almost in the near-infrared spectral range ( nm) in a single exposure. The GIANO-B spectrometer bench with optical elements and the detector array are enclosed inside a vacuum chamber, which is cooled down to cryogenic temperatures using liquid nitrogen. The chamber s pressure and temperature are continuously monitored and controlled through a number of sensors and a programmable logic controller. The spectrometer chamber is located near the Telescope Nasmyth focal station. For a higher mechanical stability, the chamber is installed on a metal structure and is attached to the fork of the Telescope mount. A warm pre-slit optical system located outside the cryogenically cooled spectrometer feeds the telescope light onto the cold slit through the entrance window on the chamber. The cold slit has on-sky dimensions of 6 x 0.5. The pre-slit also delivers the light from the calibration unit to the spectrometer. The GIANO-B spectrometer detector is a HgCdTe HAWAII x 2048 pixel array. The pixel size is 18 µm with an on-sky scale of approximately 0.25 throughout the array, and the spectrometer slit width on the detector is roughly 2 pixels. The detector read-out noise is 5 electrons/pixel, the gain is 2.2 electrons/analogue-to-digital-unit, while the dark current is 0.05 electrons/second/pixel. Even if the dark current were not subtracted the combined technical detector noise is small in comparison to the statistical photon noise that scales proportionally to the square-root of the accumulated flux. 3 Impact of photon noise on spectrometer calibration Statistical photon noise represents a fundamental limit to any spectrometer calibration. In our case photon noise largely dominates over technical detector noise such as dark current or read-out noise. For the presently obtained calibration spectra we estimate that photon noise fundamentally limits the best attainable precision to 20 cm/s, which agrees well with the found precision of 25 cm/s. The method used for this estimate, follows the derivation by Bouchy et al. (cf. Ref. 48) and takes into account the quality factor Q spec of the spectrum and the fundamental photon noise A i, where A i is the detected intensity at pixel i. The quality factor Q spec is independent of the spectral flux and is a measure of the spectral richness of the spectrum. Spectra with a high number of spectral features with steep slopes will have a higher Q spec in comparison with spectra composed of fewer or less steep spectral features. The expected radial velocity precision δv rms may then be written as δv rms c = 1 Q spec F (1) where c is the speed of light and F = i A i is the total flux. For a given spectrum with a certain quality factor, δv rms is proportional to F 1, which is the expected behaviour. The quality factor 4

6 a MLL f rep lock Frequency stability of astrocomb (MHz) 10 cm/s 1 cm/s MLL f 0 lock CW laser lock MW synthesizer Rb clock 10 s exposure b Exposure time (s) Phase noise (dbc/hz) Soliton MW synthesizer Frequency (Hz) Figure 1: Short-term stability of the astrocomb. (a) Effective impact of individual technical components on the astrocomb s stability. The horizontal dashed lines indicate the stability level required for spectrometer calibration on the level of 10 cm/s and 1 cm/s, respectively. For exposure times of 1 s or longer a calibration precision of below 1 cm/s can in principle be reached with the present system. The exposure time of 10 second (marked by a vertical line and red dot), which was used in the present work is largely sufficient to support beyond-state-of-the-art calibration. All data has been measured except for the performance of the commercially available Rb clock, which is specified by the manufacturer and corresponds to what is routinely achieved in Rb clocks. (b) Phase noise of the microwave synthesizer in comparison to the soliton s repetition rate phase noise (both at 24 GHz). The soliton s repetition rate was detected in a 1 nm wide span in the wing of the spectrum at 1515 nm. 5

7 Q spec is defined as Q spec = i λ 2 i ( A i/ λ i ) 2 A i F (2) It can intuitively be seen from Equation 2 that a higher number of spectral features with a strong wavelength λ dependence will result in a higher value of Q spec. Based on the experimentally recorded comb spectra providing A i and λ i (the wavelength at pixel i) the radial velocity precision is estimated according to Equations 1 and 2. While the flux F can not be increased, as otherwise the detector would saturate, a higher Q spec can be obtained using broader calibration spectra. 6