Laser scheme and setup

2.3.2.1 Overview

Based on the commensurate-wavelength design, the probe laser at 780 nm can be generated from frequency doubling of a 1560 nm source laser, ensuring inherent frequency locking of the two lasers. Thanks to mature Telecom photonic technologies, powerful and reliable lasers are readily available at 1560 nm. In fact, Telecom based 780 nm laser sources for cold-atom applications have been developed and met success (e.g. muQuans and MenloSystems) due to the robustness of an all-fibre setup.

Our setup¹⁵ also exploits fibre-based 1560 nm laser, laser amplifier, and components (Fig. 2.22). A fibre injected periodically-poled lithium niobate (PPLN) crystal generates frequency-doubled 780 nm laser into free-space, one part to reference the source laser via a modulation transfer spectroscopy (MTS) [126, 127] on Rb vapour.¹⁶ The two wavelengths are finally combined in free-space to be injected into the science cavity. For the auxiliary cavity, for now we only inject 1560 nm laser through direct fibre mating.

One feature of the cavity assembly is that the two cavities are mounted as close as possible on the same pair of piezo stacks, such that the thermal and mechanical perturbations to the cavity length are largely in common. One can envisage that by stabilising one cavity, the other is also stabilised. In other words, we could have a stabilised science cavity with only 1560 nm light in the auxiliary cavity. We shall discuss the feasibility later, but in general, a combination of locking both cavities is necessary, as outlined in Fig.2.20.

15Mostly built by Ralf Kohlhaas

16The MTS resembles a standard SAS but gives a zero-background error signal, which is dominated by the cycling transitions.

1560 nm laser Auxiliary cavity

780 nm laser Frequency doubling

correct

Science cavity Probes

Fixed connec�on Rb lock

PDH lock PDH lock

Figure 2.20 Schematics of lasers and cavity stabilisation for cavity-QED experiments.

The fixed connection between the two cavities is subject to residual thermal drift, which can be overcome by a “two-cavity interlock” (Sec.2.3.6).

2.3.2.2 Laser frequencies

Frequency reference To implement QND measurements of Sz in the dispersive regime, the cavity resonance is detuned in between the transitions 5S_1/2(F = 1) → 5P_3/2 and 5S_1/2(F = 2) → 5P_3/2, where we have ignored the smaller hyperfine splittings of the excited state. As the detuning determines the atom-cavity coupling for the two clock states, a precise and stable adjustment of the cavity frequency is required. The probe laser frequency should also be independently tunable, to vary the detuning to the cavity mode. As none of these frequencies is close to a particular transition of⁸⁷Rb, we instead lock the laser to the cycling transition of⁸⁵Rb (F = 3 → F⁰= 4), which is close to our target. At the same time, possible leakage resonant with the atomic transitions is avoided.

The frequency relations of the double-wavelength system are better depicted as a function of the cavity length, as shown in Fig.2.21. For the science cavity, our target mode is ∼ 2 GHz away from the ⁸⁵Rb reference at 780 nm. At the same time, it is about 800 MHz away from the laser at 1560 nm.¹⁷ The probe laser is generated by an electro-optical modulator (EOM), with the unwanted carrier and red sideband being sufficiently filtered by the cavity.

Its power and frequency are hence easily tunable. To stabilise the cavity at the target, we employ standard Pound-Drever-Hall (PDH) techniques using the 1560 nm mode.

PDH scheme for the science cavity We can directly apply PDH modulation at 800 MHz and lock the cavity to the blue sideband. In fact, this is the only choice for satisfying another crucial requirement of the experiment: the 1560 nm locking light has to be weak enough to have negligible trapping effect. Only by sending a weak sideband into the cavity could we minimise the intra-cavity power while retaining a workable PDH signal. The noise limit of the setup is analysed below.

PDH scheme for the auxiliary cavity Since the two cavities are not independently tunable, the resonance frequencies are determined (within one FSR) when they are glued, which was not fully controllable. In our case, the resonance frequency of the 1560 nm modes differ by about 35 GHz. Therefore, to stabilised the science cavity with the auxiliary cavity, the offset of the latter need to bridged.

17Half of 2 GHz, plus 170 MHz offset due to the fact that the cavity is not simultaneously resonant at 780 nm and its precise double wavelength.

780 nm

1560 nm

1560 nm

Science cavity

Auxiliary cavity 0.8 GHz PDH

35 GHz

Frequency ( - cavity length, a.u.) 1 GHz PDH 3^rdSB

target mode

85Rb lock

0.4 GHz AOM

F=2 F’=3 F=1 F’=2

2.4 GHz probe SB

locked laser

locked laser

Figure 2.21 Cavity probing frequencies of the two cavities. The frequency scales are different by a factor of 2 for 780 nm and for 1560 nm in the horizontal axis, but correspond to the same change in cavity length.

As shown in Fig. 2.21, we generate a 35 GHz sideband (third order sideband from a strong drive at 15 GHz by an EOM) to bridge the frequency offset. Another modulation at about 1 GHz is added for the PDH lock. Since now we can lock to the “carrier” (the third sideband of the laser), the PDH modulation frequency is not constrained. In practice we tune this frequency to tune the phase of the PDH error signal (about 1 GHz).

This PDH lock serves as a complementary stabilisation method. Certainly, we can lock the science cavity with its own 1560 nm mode, which is more reliable. However, despite the effort to minimise the locking light power, the atoms will always be perturbed by it.

Alternatively, we can rely on locking the auxiliary cavity, while the stabilisation is subject to residual drift between the two cavities. This latter scheme will be discussed in detail in Sec. 2.3.6.

2.3.2.3 RAM of fibre EOMs and temperature stabilisation

We utilise fibre EOMs for large modulation depth and bandwidth. However, they generally suffer more from residual amplitude modulation (RAM) compared to free-space models. One well known cause is the interference effect between phase-modulated light (polarised along the e-axis of the crystal) and the un-modulated light (polarised along the o-axis). This can happen if the input polarisation is not perfectly aligned with the crystal e-axis¹⁸ [128], which is generally the case in a fibre EOM pre-aligned by the manufacturer. Normally this misalignment can no longer be corrected.

Upon demodulation of the detected reflection, RAM contributes a DC offset to the PDH signal. Fluctuation in the RAM amplitude is directly translated into a fluctuating offset that shifts the locking point. In the case of a large offset compared to the signal itself, the lock can be even rendered unstable. Nevertheless, as an interference effect, the RAM also depends on the phase shift φeo between the e- and o-light in the crystal, which is affected by many parameters. It can be shown in a simple model that the RAM vanishes when φeo= 0.

Experimentally it can be achieved by adjusting the temperature of the crystal or by applying

18In a simple theoretical model, the RAM occurs after a final polariser. However, we observe RAM directly at the output fibre of the EOM. More complicated processes (e.g. polarisation dependent loss) might have taken place.

Keopsys

Figure 2.22 Schematics of the complete laser setup for cavity probing and stabilisation.

Here we show direct PDH locking of the science cavity. Electronics are shown in grey. APD:

avalanche photodiode; DM: dichroic mirror; FPD: fast photodiode; PZT: piezoelectric stack;

SPCM: single photon counting module; TEC: thermoelectric cooler.

a DC electric field [128,129].

In our setup, one of the EOMs (EOSPACE PM-5V5-UV) exhibits a very strong RAM.

∼0.1℃ change can render the RAM from maximum to minimum. As one simple solution, we have implemented passive temperature control of the EOM. The stability of our temperature control limits the fluctuation in RAM to an acceptable level (∼ 0.01 V for a signal of ∼ 0.4 V).