Field of the Invention

This invention relates to a method and apparatus for controlling frequency of a laser, and more particularly, but not exclusively, to a method and apparatus for locking a laser to an absolute reference frequency.

Background of the Invention

Saturated absorption spectroscopy is a ubiquitous method of frequency stabilizing diode lasers in many areas of atomic physics, such as spectroscopy, atomic clocks, laser cooling and Bose-Einstein condensation. Several methods for obtaining an error signal from an atomic transition are in use. These generally rely on modulation of either the laser frequency, b\ \ arying the laser current or modulation with an acousto-optic modulator (AOM), or by modulating an atomic reference source and subsequent electronic demodulation to produce the error signal required for locking,

Each of the above previously proposed techniques has strengths and weaknesses. For example, modulating the laser frequency by directly modulating the current, while simple and inexpensh e, suffers because the applied dither is on all of the light — the light used for locking as well as the light used for the experiment. One can circumvent this by splitting off a portion of the light and sending it through an AOVI, Modulating the AOM will cause a frequency modulation only on the portion of the light that is used for locking. While effective, the cost of an AOM and its dm ing electronics must be included in even laser that is locked directly to an atomic transition. Recently, modulation-free differencing techniques ha\ e come into use. whereby an error signal is produced by subtracting two frequency or phase shifted signals generated from the same atomic reference source. Modulation free schemes have the potential advantage, over more traditional methods, to do away with the need for lock-in electronics and the various modulation apparatus, such as AOMs and magnetic coils.

However, modulation free schemes are generally very sensitive to alignment and vibration.

While all of the above mentioned locking techniques work in producing an error signal which allows a laser to be locked, AOM modulation is the most common method in use and any alternative scheme for locking a laser will be compared to it.

Preferred examples of the invention seek to overcome or at least alleviate the above disadvantages associated with conventional methods and apparatus for locking lasers.

Summary of the Invention

In accordance with one aspect of the present invention, there is provided a method of controlling a frequency of a laser including the steps of: phase modulating a beam from the laser by reflecting the beam with a mirror oscillating at a drive frequency to provide a phase modulated beam having a main frequency and two sideband frequencies; processing the phase modulated beam by passing it through a reference material for relating the frequencies of the phase modulated beam to a reference frequency of the reference material by saturated absorption spectroscopy; detecting the processed beam using a photodetector for giving a combined beat signal indicative of the reference material; demodulating the combined beat signal at the drive frequency to produce an error signal; and adjusting the frequency of the laser according to the error signal whereby the frequency of the laser is controlled to correspond to the reference frequency.

In accordance with another aspect of the present invention, there is provided an apparatus for generating an error signal for controlling a frequency of a laser, including a mirror oscillating at a drive frequency for reflecting a beam from the laser to phase modulate said beam whereby the phase modulated beam has a main frequency and two sideband frequencies, reference material arranged for processing the phase modulated beam by passing it through the reference material for relating the frequencies of the phase modulated beam to

a reference frequency of the reference material by saturated absorption spectroscopy, a photodetector for detecting the processed beam to give a combined beat signal indicative of the reference material, and a lock-in amplifier for demodulating the combined beat signal from the detected beam at the drive frequency to produce an error signal, wherein the error signal is able to be used for controlling the frequency of the laser to correspond to the reference frequency.

Preferably, the apparatus further includes a feedback loop for adjusting the frequency of the laser according to the error signal.

Preferably, the reference frequency is an atomic transition frequency or molecular transition frequency of the reference material. More preferably, the reference material is an atomic vapor. Even more preferably, the reference material is contained in a cell.

Preferably, the mirror is piezo-electrically actuated to the drive frequency. More preferably, the mirror is attached to a piezo-electric transducer. Even more preferably, the piezo-electric transducer is operated at the drive frequency by a signal generator.

Preferably, the error signal is a zero crossing error signal such that the output of the error signal has a different sign according to whether the laser frequency is above or below the reference frequency.

Preferably, the apparatus for generating an error signal for controlling the frequency of the laser is provided as a unit such that the unit receives the beam from the laser as an input and provides the error signal as an output. Even more preferably, the reference material is interchangeable with other reference materials having other reference frequencies such that the unit can be used to control the frequencies of a variety of lasers at a variety of reference frequencies. In one form, the unit is able to be used with a range of interchangeable cells having different reference materials.

Through phase modulating a laser beam using the mirror mounted on the piezo-electric

transducer (PZT), there is provided a robust, simple and inexpensive system for producing the modulation required for locking; an approach that results in true zero crossing error signals, is far simpler to implement than AOM-locking, and costs more than an order of magnitude less than AOM-locking.

Brief Description of the Drawings

The invention is described, by way of non-limiting example only, with reference to the accompanying drawings in which:

Figure 1 is a schematic diagram of an apparatus for controlling frequency of a laser; Figure 2 is a graph of Volts versus Time showing typical data obtained in using the apparatus of Figure 1 to obtain an error signal for controlling the frequency of a laser;

Figure 3 is a graph of Intensity versus Frequency showing resonances of a piezo- electric-transducer (PZT) mounted mirror of the apparatus shown in Figure 1 ;

Figure 4 is a graph of Intensity versus Frequency showing the beat signal from two lasers, each using PZT locking;

Figure 5 is a perspective view of an experimental embodiment of an apparatus for controlling frequency of a laser; and Figure 6 is a top view of a PZT-mounted mirror of the apparatus shown in Figure 5.

Detailed Description

PHASE MODULATION It is known that light can be phase modulated by reflecting it off of a moving mirror.

For monochromatic radiation phase modulation is similar to frequency modulation. This can be seen by considering monochromatic light with an electric field given by, E = EQ COS( ω f), where E ₀ , is the amplitude and ω the frequency of the unmodulated electric field which is normally reflected off of a mirror oscillating with an amplitude A and frequency ω ,„. This will result in phase modulation, cos( #,„()• If we let δ = 2 πA/λ then the resulting phase

A modulated electric field is:

E = EQ cos(ω t + δ cos ω _m t) (1)

= E ₀ [J _Q (δ ) cosω t (2)

∑ (A)^J _j (S ) Sm(CO +jω _m )t y=±i,±3... + ∑ (-I) ¹ W COS(^ ^y +j ω _m )t] y=±2,±4...

, where the J's are Bessel functions. In the limit of small phase modulations (δ « 1), Jo(δ ) « 1 , J _±] ( 5 ) « ± — and the above expression reduces to;

E w Eo[cos ωt — [sin(c; + ω _m )t + sin(c? - «„,)/] (3)

, which is the original, unmodulated wave plus two, small sidebands, ± ω „, away from the unmodulated beam, and is the same result as obtained by weak frequency modulation.

Photodetectors measure < E ² >, the time average of the electric field and are unable to measure phase, thus dithering techniques are used to enable phase detection. If phase modulated light passes through an atomic vapor and is then incident upon a photodetector, the resulting signal will be due to the mixing of the three frequencies, the carrier and the two sidebands ( ω , ω + ω _m , ω - ω _m ).

The atomic vapor is used so as to provide an external frequency reference to which the frequency of the laser is able to be tuned. When the beam from the laser strikes a sample of atoms, it will trigger resonant jumps of electrons in the atoms provided that the frequency of the laser light coincides with the frequency of a spectral line of these atoms. Thus, the laser light will be strongly absorbed if, and only if, its frequency coincides with that of an atomic spectral line. As such, by passing the laser light through the atomic vapor it is possible to relate the frequency of the laser light to a reference frequency of a specific spectral line of the atoms of the vapor material to enable tuning of the frequency of the laser light to that reference frequency.

The detector signal will be a superposition of the 3 beat signals, one between the carrier and the upper sideband, one between the carrier and the lower sideband and one between the two sidebands. In the limit of small phase modulation, the beat signal between the two sidebands is small compared to the other two beat signals, and may be ignored. It is the combination of the two beat signals, that when demodulated, result in the error signal. If the carrier is on resonance, the beats resulting from the sidebands and the carrier cancel and there is no signal at the modulation frequency, while if the carrier moves off resonance, the resulting error signal is due to a difference in the strength of the sidebands after passing through the atomic vapor. The result is a true zero crossing error signal after phase sensitive detection at the modulation frequency. The zero crossing of this error signal is immune to intensity variations in the laser or the optical depth of the medium. By virtue of the zero crossing error signal providing an output which has a different sign (ie. +ve or -ve) depending on whether the laser frequency is above or below the reference frequency, the error signal is able to be used for indicating in which direction the laser frequency needs to be adjusted in order to correspond to the reference frequency.

TECHNIQUE

For frequency stabilizing a laser to an atomic transition the apparatus shown in Figure

1 is used. This figure shows a schematic diagram of one setup used for creating modulated light for saturated absorption spectroscopy. PBS = polarizing beam splitter, λ /4 = quarter wave plate, ND = neutral density filter, and Ml and M2 are mirrors. For the version shown in the figure, both the probe and pump beams are modulated. Doing away with the top of the system (PBS, λ /4 and Ml), and modulating just the probe beam (placing the PZT on mirror

2), yields similar error signals to those produced by the configuration of Figure 1 and minimizes the amount of optics devoted to locking.

A small portion of laser light is split off from the main beam going to the experiment.

This laser light is phase modulated by Ml, which is attached to a PZT, and is then sent to a standard saturated absorption spectrometer. The modulated saturated absorption signal is converted to an error signal using a commercial lock-in amplifier (SRS 510) which demodulates the photodiode signal at the PZT drive frequency, to produce an error signal.

Typical data are shown in Figure 2 for saturated absorption of the 5 ² S , F = 2 -> 5 ² P ₃

I 1 transition for ^ ¹ Rb (lower trace) and the corresponding error signal. The transitions are labelled, F — »F'. For clarity, the saturated absorption signal's Doppler background has been subtracted, it has been offset from zero and multiplied by 20.

The PZT-mounted mirror can be placed almost anywhere, however it is preferred to use the PZT-mounted mirror with normally incident light, in order to minimize pointing errors that result from the moving mirror. For the work that is reported here, the PZTs used are high voltage (1,000 V) PZTs from Piezomechanik, ring shaped, with an outer diameter of 2.5 cm to match the diameter of the mirrors. The PZT is attached to a brass mount and the mirror is . attached to the PZT. A massive mount is preferable, helping to ensure a higher resonance frequency and larger mirror displacement. A thin layer of cynoacrylate glue is used for attaching the mount, PZT and mirror together. The brass mount is designed to fit into a standard mirror mount, where it is held in place by a set screw. More secure methods, such as putting threads on the brass and the mirror mount, may be used.

The applicant has determined that that when the PZT is driven by a standard function generator, with a sine wave with a peak to peak voltage of 8 Volts, at the most responsive of the PZT resonant frequencies, there is sufficient modulation to create a strong error signal from the saturated absorption system. Two identically mounted PZT-mirrors were tested, both having sharp resonances near 30kHz. The resonance of the mount-PZT-mirror system can be found by using the PZT modulated mirror as one mirror in an interferometer and observing fringe amplitude as a function of the frequency with which the PZT is driven (Figure 3).

Figure 3 shows the high frequency response of the PZT when attached to the brass mount and the mirror and making up one corner of a Mach-Zehnder interferometer. The resonances near 3OkHz result in sufficient displacement for creating an error signal.

Alternatively, the modulated mirror can be placed into a saturated absorption system and the error signal observed for different driving frequencies. The error signal will be substantial only at the resonant frequency.

The applicant has locked two external cavity diode lasers, a Toptica TA 100 and one built in-house, by mirror modulation. The error signals are symmetric about zero, hence need no electronic offset to achieve this, and are stable over many hours. Making an optical beat measurement between the Toptica and the homemade laser yields a peak with a width of 1.9

MHz, which is a convolution of the widths of the two lasers (Figure 4).

Figure 4 shows the beat signal from two lasers, each using PZT locking. One laser was locked to the ^s7 Rb2 -» 1,2 crossover and the other to the 2 -> 1 ,3 crossover (Figure 2). These crossover peaks are separated by 78.5 MHz. The full width at half maximum (3 dB) of the beat signal is 1.9 MHz, yielding a laser linewidth of 1.3 MHz. 1 ,000 scan average, resolution bandwidth of 100 kHz, video bandwidth of 10 kHz.

Assuming the lasers have identical lineshapes, the full width at half maximum of the lasers, based upon the beating data, is 1.3 MHz. This linewidth is consistent with the free running linewidths of each laser implying no active narrowing due to the feedback electronics used. Using the PZT-locking technique, lasers typically remain locked for a day, as evidenced by the Toptica, maintaining a rubidium magneto-optic trap for the production of Bose-Einstein Condensates.

The applicant has tested the suitability of a small, low voltage (150 V) PZT (ThorLabs) for use with piezo-locking. Due to its small size, it was attached to a 1.25 cm, rather than a 2.5 cm, diameter mirror. The mirror and PZT were then attached to the same type of brass mount and optical mount as used with the high voltage PZTs. A peak to peak driving voltage of 2 V, applied at resonance, resulted in an error signal comparable to that produced by the high voltage PZT. An advantage of the low voltage PZT is that it may be driven directly by the lock-in amplifier. However, for this particular PZT, the resonant frequency is just under 3 kHz, too low to allow the suppression of acoustic disturbances.

An experimental embodiment of an apparatus for controlling frequency of a laser is shown in Figure 5. More particularly, this figure shows a practical embodiment in which a

mirror 10 mounted on a PZT 12 is used for phase modulating laser light in order to lock a laser to an atomic transition frequency of reference material. The reference material is in the form of atomic vapor contained in a vapor cell 14. A close-up view of the mirror 10 mounted on the PZT 12 is shown in Figure 6.

The applicant has demonstrated modulation-based frequency locking of a diode laser, utilizing a piezo-electrically actuated mirror to create an error signal from saturated absorption spectroscopy, hi one particular experiment, lasers stabilized to Rb hyperfine transitions had a FWHM of 1.3 MHz and typically remained locked for many hours.

Methods and apparatus of examples of the present invention combine the advantages of simplicity, performance and price — factors which are usually considered to be mutually exclusive.

The applicant has determined that phase modulation produced by a PZT modulated mirror is a practical method for locking a diode laser to an atomic transition. It is inexpensive, easy to implement, robust, and yields true zero crossing error signals, allowing lasers to be locked for many hours at a time. PZT locking can be used for other lasers as well as other atomic species.

The above embodiments have been described by way of example only and modifications are possible within the scope of the invention.

APPENDIX - References of related art

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3. K.L. Corwin, Z-T. Lu, CF. Hand, RJ. Epstein, and CE. Wieman. Frequency- stabilized diode laser with the zeeman shift in an atomic vapor. Appl Opt. ,

37:3295-3298, 1998.

4. CL Sukenik, H.C Busch, and M. Shiddiq. Modulation-free laser frequency stabilization and detuning. Opt. Comm., 203:133-137, 2002.

5. S.E. Park, H. S. Lee, T.Y. Kwon, and H. Cho. Dispersion-like signals in velocity- selective saturated-absorption spectroscopy. Opt. Comm., 192:49-55, 2001.

6. N.P. Robins, BJJ. Slagmolen, D.A. Shaddock, J.D. Close, and M.B. Gray. Interferometric, modulation-free laser stabilization. Optics Letters, 27: 1905, 2002.

7. P. Van der Straten E.D. Van Ooijen, G. Katgert. Laser frequency stabilization using doppler-free bichromatic spectroscopy. Appl. Phys. B, 79:57, 2004.

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