An Ultra-Stable Laser System for Coherent Atomic Interrogation

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A New Laser System for Cooling Mercury Atoms

Cooling neutral mercury atoms requires continuous wave laser light at 254 nm with relatively narrow linewidth (on the order of 10 kHz) and high enough power (on the order of 50 mW to well saturate the atomic transition). What is more, building an optical clock adds to the equation a constraint of robustness and reliability, for continuous operation over several hours, days or even months! I will describe in this chapter the technical solutions that I have found to meet these challenging requirements.
Historically, the development of SYRTE’s mercury optical lattice clock has been hampered by recurrent problems with the cooling laser system. Prior to the beginning of this thesis, before commercial high-power and narrow linewidth Ytterbium-Doped Fiber-Amplifier (YDFA) technology was available, the cooling light was produced by a fre-quency quadrupled thin disk laser1. This laser was very difficult to op-erate, with a warm-up time of several hours and frequent mode hops, which prompted us to think about a better solution.
During the course of this thesis, I designed a laser architecture based on newly available commercial YDFA technology and two sys-tems were built for cooling mercury 199Hg atoms on the 1S0 ! 3P1 transition. One of these systems is used to power the 3D-MOT (see Section 1.2), while the second will be used to power the 2D-MOT, and it is frequency locked onto the first one (see Sections 1.2.4 and 2.3.1).

Requirements

In this section, we study requirements for our cooling light system in order to efficiently cool down mercury atoms in a magneto-optical trap and perform atom counting by fluorescence detection. From these prerequisites, we will draw a set of specifications, which we will use to design a suitable architecture for our purpose.

Spectral purity

As seen in the Introduction, the linewidth of the cooling transition is about 1.3 MHz. Therefore, to cool efficiently the atoms (down to the Doppler temperature of 30 K), we have to build a laser system in the UV at 254 nm, with a linewidth narrow with respect to 1.3 MHz. If we take a factor 10 of margin, we therefore need to build a system with linewidth smaller than 100 kHz in the deep UV.
To our knowledge, no CW laser source with this kind of linewidth is available at 254 nm, and a similar argument applies for a source at 2 254 nm = 508 nm. Consequently, we anticipate that we will start with a laser system working in the infrared (IR) around 1015 nm, which will be doubled twice to reach the desired wavelength.
Taking into account that frequency quadrupling an optical signal increases the linewidth (assuming that said linewidth is limited by white phase noise) by a factor 16, we conclude that we need a linewidth of the original IR laser below 6 kHz, which sets a significant technical constraint.

Laser power

The power requirements for cooling neutral atoms is usually set with respect to the saturation intensity [69].
For mercury, the value of this parameter is 102 W/m2. Since we have 3 MOT arms, we would ideally want I ’ Isat for each of the MOT arms, we would therefore need to have Itot ’ 306 W/m2. Assuming a beam area of 1 cm2, we therefore need more than 30 mW of total laser power at 254 nm, reliably on a time scale of several hours to several days. We expect that more than 50 mW should be reachable with our setup.

Architecture of the Cooling Laser

Taking into account the specifications established above, I have devised the architecture presented on Figure 2.1. The laser light is generated by a home-built external cavity diode laser (ECDL) in the IR at 1015 nm, providing a narrow spectrum before quadrupling.
Figure 2.1. Overall cooling laser architecture. The narrow linewidth ECDL at 1015 nm is amplified in an YDFA, and frequency doubled twice to 254 nm. The light at 254 nm is locked to the cooling transition via saturated absorption spectroscopy in a Hg cell (see text for more details).
The light from this laser is injected into a Ytterbium doped fiber amplifier (YDFA), which allows us to get high enough power before frequency quadrupling while keeping the narrow linewidth properties of the ECDL.
The amplified light is then frequency doubled to 507 nm in a sin-gle pass configuration with a Periodically Poled Stoichiometric Lithium Tantalate (PPsLT) crystal, and subsequently doubled in a resonant doubling cavity containing a -Barium Borate (BBO) crystal.

External-Cavity Diode Laser

The first stage of the system is designed to have a narrow linewidth of at most a few kHz, tunable frequency output and a high enough power to feed the subsequent amplifier. It is a home-built ECDL 42 A New Laser System for Cooling Mercury Atoms mounted in Littrow configuration (recoupling of the 1st diffracted or-der from the grating into the diode) that I designed and assembled at the beginning of my PhD. A scheme of the ECDL can be seen on figure 2.2.
Figure 2.2. Scheme of the ECDL seed laser for the cooling laser system. The home-made aluminum enclosure is shown in blue. TEC: temperature controller, HV: high-voltage, PZT: piezo-electric transducer.
External-cavity diode lasers offer high frequency tunability over dif-ferent ranges: coarse tunability on the nm scale with the grating angle thanks to the spectral dispersion of the reflected light on the grating, finer tunability by mounting the grating on a Piezo-Electric Transducer (PZT), on the hundreds of MHz scale, with up to a few kHz bandwidth, and finally fast tunability by reacting weakly on the current for high-bandwidth locking of the laser. This makes it a very versatile and tunable laser, with narrow linewidth, ideal as a seeder, provided we can keep it single frequency [90].
Since we need a linewidth below 6 kHz, we have chosen a long extended cavity architecture, with a distance between the diode chip (TOPTICA single-frequency diode laser, specified linewidth 1 MHz) and the grating (Edmund Optics) of 12 cm used in Littrow configura-tion.
With such a long cavity, I needed to make sure that the seeder would keep a single mode behavior over a wide enough range of fre-quencies (several GHz ideally). To that end, the laser diode is mounted with thermal glue on a copper piece and glued to a Peltier element for active temperature stabilization and frequency tuning. The optical setup (diode plus grating) is contained in an aluminum enclosure (also home-built) which can also be temperature stabilized if needed. Care was taken to avoid mechanical resonances, by putting the grating on a brass piece, and by setting the whole aluminum enclosure on spring washers. Finally, I put the breadboard containing the aluminum box (see Figure 2.3) in yet another box that I assembled with aluminum profiles and PVC foam, and mounted on sorbothane pads for further vibration isolation from the rest of the environment.
The seed laser outputs close to 15 mW of light at 1015 nm, and by beating it with the previous cooling laser system (Versadisk), we have verified that its linewidth is below 1 kHz on short timescales.

Laser amplifier and single stage doubling to 507 nm

The 2-stages amplifier yields an overall gain of 28 dB (from 15 mW to 10 W). Experimentally, I had to find a trade-off between a long ac-tive (Yb-doped) fiber of the amplifier, yielding a higher gain, and a low enough amount of ASE (Amplified Spontaneous Emission), performing successive fiber cutbacks while monitoring the output power and ASE spectrum.
Several stages of optical isolation have been installed in the final manufactured product to reduce the risk of damage to the pumps or the seeder, which might occur due to Q-switching in the fiber amplifier. In spite of these precautions, the amplifier had to be shipped back to the manufacturer several times during the course of the PhD because of damages to the fiber gain medium.
The resulting 10 W of 1015 nm light are focused onto a oven-stabilized PPsLT crystal for frequency doubling to 507 nm. The fun-damental pump signal at ! is separated from the frequency doubled signal at 2! by a dichro¨ıc mirror and damped into a beam-dump. The overall architecture of the YDFA system is shown on figure 2.4.
Thanks to the fibered technology, this system necessitates almost no warm-up time, and can operate reliably for several months, after which we have found that the seed laser usually acquires a slightly multimode behavior and the recoupling into the diode needs to be ad-justed via realignment of the grating.
Furthermore, it can be installed in a dedicated rack, freeing pre-cious real-estate on the main optical table.

Frequency doubling to 254 nm

The final step of our cooling laser apparatus is frequency doubling to 254 nm to couple to the 1S0 ! 3P1 cooling transition.
For this, we use resonant doubling in a cavity in a BBO crystal. BBO was chosen for its high doubling conversion efficiency, trans-parency in the deep UV, and more importantly because it has a high damage threshold and durability in the UV, which are absolutely cru-cial features for our application. The cavity is realized in a bow-tie configuration, with a total length of 84.2 cm and a waist at the posi-tion of the crystal of 30 m. The finesse is approximately 220.
A sidelock scheme is used to lock the cavity (reacting on one of the flat mirrors of the cavity glued to a piezo-elctric transducer) to the side of the optical resonance with a tunable offset which allows us to easily adjust the UV power sent to laser-cool the atoms. One of the drawback is that the sidelock scheme is intrinsically asymmetric (we lock to one side of the fringe), which creates and asymmetric spectrum of the generated UV light at the output of the cavity. However, since the cooling laser has been designed to have a linewidth much smaller than the decay rate of the cooling transition, we don’t expect this to be an issue for the atomic cooling efficiency. Figure 2.5 (a) shows a plot of the optical power output from the doubling cavity at 254 nm as a function of the offset of the cavity sidelock. From an input 2 W of light at 507 nm, we get a peaked signal on the locking photodiode of the cavity of 2.5 V. If we take the graph of Figure 2.5 (a), fit it with a linear model and extrapolate to this value, we estimate that locking at 2.5 V on the sidelock would yield 370 mW of light at 254 nm, but at the risk of damaging the doubling crystal and UV optics in a matter of minutes. We therefore operate with a more reasonable sidelock offset between 300 and 350 mV, giving a usable ’ 50 mW of UV light, fulfilling the requirements set in Section 2.1.
Moreover, it has been empirically observed that operating in a pure oxygen environment reduces the risks of UV-damage to the BBO crys-tal as well as the optics of the doubling cavity. A airtight aluminum enclosure hooked to a medical-grade oxygen bottle has therefore been designed during the PhD thesis of R. Tyumenev and surrounds the cavity with a well-controlled quasi-pure O2 environment. In the course of my PhD, this design has been improved to include a new crystal holder and positioner which can be controlled without having to open the aluminum enclosure, which was a source of contamination of the crystal environment in the previous system. The new doubling cavity is shown on Figure 2.5 (b).

Locking to the cooling transition via saturated-absorption spectroscopy

In order to tune the laser at a tunable frequency offset from the cooling transition, it needs to be offset-locked to the resonance via saturated absorption spectroscopy. Saturated-absorption is a tech-nique used to obtain narrow-line optical lineshapes for locking or spec-troscopy, free of 1st order Doppler effects.
A strong pump beam (with wave-vector kl ) is sent through a ther-mal gas of atoms and saturates the transition of interest. Let us con-sider the particular case where this beam is slightly detuned with re-spect to the atomic resonance by a quantity = 0 where is the laser beam frequency and 0 the atomic transition frequency.
We see that in order to satisfy equation 2.3, atoms with a velocity ~v will be pumped to the excited state, creating another hole in the atomic velocity distribution centered around ~v.
If the 2 counter-propagating laser beams are now at resonance with the atoms ( = 0), then the only way to satisfy both equation 2.2 and equation 2.3 is that both laser beams interact with atoms for which ~v = 0, creating an absorption feature in the velocity distribution which is the sum of the contribution from both laser beams centered around ~v = 0 and therefore free of 1st order Doppler effects (further details on saturated-absorption locking can be found in [92]).
Picture 2.6 (a) shows the overall locking setup of the cooling sys-tem. AOM1 is used to dynamically control the detuning of the light going to the Magneto-Optical Trap for the capture and compression phases, as discussed in Section 1.2.2. It works around 180 MHz, with a digitally tunable detuning which varies between -1.5 and -5.5 . The detuned light is then sent to AOM2, which is also cen-tered around 180 MHz and used to generate a modulation at 300 kHz for frequency-modulation locking of the ECDL to the Doppler-free saturated-absorption feature shown in blue on Figure 2.6 (b).
Figure 2.6. (a) Scheme of the locking to the cooling transition via saturated absorp-tion spectroscopy. and (b) Experimental signals. The blue trace is the Doppler-free saturated-absorption signal, and the red trace is the dispersive error signal generated by the modulation of the beam with AOM2. Both signals are observed by scanning the frequency of the laser across the atomic resonance.
In order to generate this signal, the modulated light is sent through a 1-mm-long quartz cell containing Hg vapor at ’ 0.25 Pa at room tem-perature surrounded by a magnetic field to resolve the fine structure of the 3P1 level. The beam incoming on the cell is split by a PBS, and the reflected part is sent to a photodiode (PD1 on the scheme) to act as a reference signal for background noise suppression.
The transmitted beam goes once through the cell, is retro-reflected on mirror M, and goes through the cell again to generate the saturated absorption signal on photodiode PD2. Its polarization is controlled by a quarter wave-plate which is tuned experimentally to balance the two photodiodes and maximize the signal to noise ratio of the Doppler-free feature. The subtracted signal from the photodiodes is then mixed with the 300 kHz modulation and serves as the error signal for the lock (red curve of Figure 2.6 (b)).
As can be seen on Figure 2.6 (a), in order to lock the laser to the Hg signal, we use a double integrator to feedback onto both the cur-rent and the PZT of the grating of the ECDL. The current allows high-bandwidth locking, and the PZT increases the capture range of the lock.

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A Second System for the 2D-MOT

The second system which we will use to run the 2D-MOT is an almost exact copy of the first one (including the ECDL seed laser), except for the slightly higher laser power (2 W instead of 1.5 W at 507 nm).
This laser doesn’t need to be tuned in frequency, since the 2D-MOT works at a fixed detuning from the cooling transition, chosen experi-mentally to maximize the loading rate into the 3D-MOT. Therefore, we have decided to implement a simple offset frequency lock between the two seed lasers with a feed-forwarding system to keep the 2D-MOT laser at a fixed detuning from the cooling transition while moving the detuning of the 3D-MOT system for MOT compression as discussed in Chapter 1.

Frequency locking of the two seed lasers for 2D-MOT operation

Since optical coherence between the two lasers is not a require-ment, we can devise a simple scheme to lock the 2D-MOT cooling laser to the atomic transition by frequency locking it to the 3D-MOT laser. The frequency lock between the two seed lasers follows the scheme of Figure 2.7.
Seed 1 is locked to the atomic transition via saturated absorption spectroscopy as described in section 2.2.3. An AOM is inserted af-ter the second seed, to generate on the photodiode (PD) a heterodyne beatnote around 180 MHz between the two ECDLs. This beatnote is fed into a frequency to voltage converter (F to U), which delivers a volt-age proportional to the frequency of the input signal. We then subtract a voltage offset from this signal to generate the error signal which we correct using a proportional-integrator gain and we feed this back onto the PZT of the second seed laser with a bandwidth of 5 kHz. The de-tails of the locking electronics, that I designed and built during my thesis are shown on Figure 2.8. I have included a few offset inputs, one of which will allow us to tune the frequency of Seed 2 directly with the program that control the rest of the experiment.
Another input is used to feed forward to the Seed 2 the detuning applied to the Seed 1. Indeed, as the frequency of the Seed 1 is mod-ulated during the MOT sequence, as described in Chapter 1.2 from 5.5 to 1.5 , this will create a perturbation on the frequency of the 2D-MOT light, since Seed 2 will follow the frequency of Seed 1.
To get rid of this issue, we use a 2nd offset input to be able to realize a feed-forwarding scheme, which we will use to null the effect of the detuning of Seed 1.
Figure 2.7. Scheme of the frequency lock between the two seeds. The AOM is used to create a heterodyne beat between the two lasers on a photodiode. The frequency differ-ence between the seeds is converted into a voltage by a frequency to voltage converter and compared to a reference, tunable offset which defines the lock point. PD: PhotoDi-ode, PBS: Polarizing Beam-Splitter, F to U: frequency to voltage converter, : error signal, PI: Proportional-Integral.
In this chapter, we consider the coherent interrogation of our sam-ple of cold atoms by the ultrastable clock laser. Scanning the fre-quency of the laser, we are able to resolve the strongly forbidden clock transition, which will provide the frequency discriminator for our clock. We will see that, using a weak probe laser well aligned with the optical lattice, we are able to probe the carrier transition free of any motional effects. In this configuration, we have recorded very high resolution spectra, and demonstrated the coherent manipulation of the internal quantum states of the atoms for probing times as long as several hun-dreds of milliseconds.
However, the effects of atomic motion in the lattice trap still need to be taken into account, as they can be a very serious issue for clock ac-curacy, creating motion-dependent lattice-related light-shifts and ex-citation inhomogeneities. Information on atomic motion and tempera-ture can be extracted from clock spectroscopy by looking at the side-band structure around the motion-less carrier transition. In lattice clock experiments, longitudinal sidebands are usually probed using a high-power (enough to strongly saturate the carrier transition) probe beam, and fitted to obtain an accurate measurement of the lattice trap depth, as well as atomic temperature [6]. However, in our experiment, the lack of power in the UV prevents us from using this technique as a diagnostic tool. However, if we introduce an angle between the probe and the lattice, transverse motional sidebands will be coupled to our interrogation laser even for relatively weak probe powers. We will use this fact to our advantage and extract useful information about the trapping potential from the frequency of the transverse sidebands.

Table of contents :

Introduction 
0.1 Optical Atomic Clocks
0.1.1 Ion-based optical clocks
0.1.2 Optical lattice clocks
0.1.3 Current and prospective applications of optical frequency standards
0.1.4 Context and objectives of my PhD work
0.2 The Mercury Atom: a Short Overview
0.3 Mercury Level Structure: the Key to a Highly Accurate Frequency Standard
0.4 Thesis Overview
1 A Mercury Optical Lattice Clock 
1.1 Overview of the Experimental Setup
1.2 Cooling of Mercury Atoms in a Magneto-Optical Trap
1.2.1 The cooling-laser system
1.2.2 3D-MOT of 199Hg
1.2.3 Vapor pressure and MOT lifetime
1.2.4 Pre-cooling with a 2D-MOT
1.3 Trapping in a 1D “Magic” Optical Lattice
1.3.1 The trapping laser system
1.3.2 Locking scheme for the lattice light
1.3.3 A build-up cavity for a deeper trap
1.3.4 Absolute frequency calibration with a frequency comb
1.3.5 Lifetime of the atoms in the lattice
1.4 An Ultra-Stable Laser System for Coherent Atomic Interrogation
1.4.1 Fabry-Perot cavity for laser stabilization
1.4.2 Ultra-stable laser setup
1.4.3 Laser noise and frequency doubling
1.5 Fluorescence Detection
2 A New Laser System for Cooling Mercury Atoms 
2.1 Requirements
2.1.1 Spectral purity
2.1.2 Laser power
2.2 Architecture of the Cooling Laser
2.2.1 External-Cavity Diode Laser
2.2.2 Laser amplifier and single stage doubling to 507 nm
2.2.3 Frequency doubling to 254 nm
2.2.4 Locking to the cooling transition via saturated-absorption spectroscopy
2.3 A Second System for the 2D-MOT
2.3.1 Frequency locking of the two seed lasers for 2DMOT operation
3 High-Resolution Spectroscopy in an Optical Lattice Trap 
3.1 Theory: Spectroscopy in a 1D Optical Lattice
3.1.1 Clock spectroscopy in the Lamb-Dicke regime
3.1.2 Structure of the clock transition
3.1.3 Rabi and Ramsey spectroscopy
3.2 Experimental Spectroscopic Signals and Their Interpretation
3.2.1 Magnetic field zeroing using clock spectroscopy measurements
3.2.2 Carrier spectroscopy of the two Zeeman sublevels
3.2.3 Control of atomic noise: implementing a normalized detection
3.2.4 Towards improved stability: high-resolution Rabi and Ramsey spectroscopy
3.2.5 Rabi flopping and excitation inhomogeneities
3.3 Estimation of the Trap Depth with Transverse Sideband Spectroscopy
3.3.1 Spectroscopy with a misaligned probe beam
3.3.2 Estimation of the trap depth
3.4 Studies of Parametric Excitation in the Trap
3.4.1 Trap depth estimation
3.4.2 Atomic temperature filtering
4 Clock Operation and Short-Term Stability Optimization 
4.1 Locking to the Atomic Resonance
4.2 Allan Deviation and Clock Stability
4.3 Fundamental Sources of Noise
4.3.1 Quantum projection noise
4.3.2 The Dick effect
4.3.3 Optimization of clock stability
4.4 Study of the Detection Noise
4.5 Estimating the Mercury Clock Stability Without Referencing
to a Second Optical Clock
4.5.1 The atoms against the ultrastable cavity
4.5.2 Stability for systematics evaluation
4.6 Stability of a Two-Clocks Comparison: Correlated Interrogation
4.6.1 Principle of correlated interrogation
4.6.2 Transfer of spectral purity via the optical frequency comb
4.6.3 Correlated interrogation – experiments
5 Ascertaining the Mercury Clock Uncertainty Beyond the SI Second Accuracy 
5.1 Clock Accuracy
5.1.1 Digital lock-in technique for studying systematics
5.2 Collisional Shift
5.2.1 Theoretical introduction
5.2.2 Experimental results
5.3 Lattice AC Stark-Shift
5.3.1 Linear shift
5.3.2 Vector shift
5.3.3 Higher order terms
5.4 Zeeman Shift
5.4.1 Linear Zeeman effect
5.4.2 Quadratic Zeeman effect
5.5 Blackbody Radiation Shift
5.6 Measurement of the Phase Chirp Introduced by the Pulsing of the Clock Acousto-Optics Modulator
5.6.1 Digital I/Q demodulation for phase estimation
5.6.2 Results and shift estimation
5.7 Other Shifts
5.7.1 Background gas collisions
5.8 Final Uncertainty Budget
6 Frequency Ratio Measurements for Fundamental Physics and Metrology 
6.1 Purpose of Frequency Ratios Measurements
6.1.1 Redefinition of the SI second
6.1.2 Time variation of fundamental constants
6.2 Detailed Experimental Scheme
6.3 Comparison With Microwave Frequency Standards
6.3.1 Hg/Cs frequency ratio
6.3.2 Hg/Rb frequency ratio
6.3.3 Gravitational redshift estimation and correction
6.4 Comparison With a Strontium Optical Lattice Clock
6.5 Measurement of Frequency Ratios via European Fiber Network
6.6 Long-Term Monitoring and Fundamental Constants

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