A Yb optical clock with a lattice power enhancement cavity

Chunyun Wang(王春云), Yuan Yao(姚远), Haosen Shi(师浩森), Hongfu Yu(于洪浮),Longsheng Ma(马龙生), and Yanyi Jiang(蒋燕义)

State Key Laboratory of Precision Spectroscopy,East China Normal University,Shanghai 200062,China

Keywords: optical atomic clock,optical lattice,optical cavity,Stark shift

1.Introduction

In the last decade, the development of optical atomic clocks has drawn wide attention since they can provide unprecedented measurement precision and uncertainty at the 10-18level.[1-4]Nowadays, optical atomic clocks play a significant role in tests of fundamental physics,[5-7]search for dark matter,[8,9]and precision measurement.[10,11]Most importantly, the international system of units (SI) of time,the second, will be redefined based on the optical atomic clocks.[12,13]Optical clocks based on a large number of neutral atoms trapped in an optical lattice (also called optical lattice clocks) have shown advantages in frequency stability.Due to thousands of atoms contributing to the signal, optical lattice clocks have lower frequency instabilities on thelevel[8,14]and thus it takes less time to achieve a measurement uncertainty of 10-18in frequency ratio measurements.[8]

However,in optical lattice clocks the lattice light usually has a large power in order to trap enough atoms, resulting in nonnegligible frequency shifts.The shifts of the ground and the excited electronic levels can be cancelled by carefully tuning the lattice laser frequency close to a magic wavelength,[15]which will largely reduce the resulting frequency shift of the clock transition.As the frequency uncertainty of optical lattice clocks has been pushed down below 10-17, high order couplings,including magnetic dipole,electric quadrupole,and hyper-polarizability should be considered.[16-19]However,the uncertainties of the frequency shift coefficients due to multipolarizability and hyperpolarizability are the key limitation when reducing the uncertainty of lattice light shift below 2×10-18.[17,20,21]One approach to accurately determine these coefficients is to measure the frequency shifts when the trap depth varies from tens of recoil energy to even thousands of recoil energy,[16,17]which challenges the output power of lattice lasers.A power enhancement lattice cavity can solve this problem.[16,18,19]Meanwhile, the implement of a lattice power enhancement cavity has three other benefits.First,due to power enhancement the lattice intensity can be kept unchanged when the lattice beam waist is increased in order to reduce the collision shift and the collision loss of trapped atoms as well.The exclusion of the frequency shifts due to atomic collision is a prerequisite in determining the higherorder lattice shift coefficients.[16,17]Second,the lattice light in the cavity is a standing wave,and the intensities of two propagating lattice beams are balanced.Thus, the frequency shift due to imbalanced lattice intensity can be ignored.[1,17]Third,due to power enhancement, it reduces the light power of the lattice laser, and thus the power consumption and size.This additional benefit is critical in transportable optical clocks for practical applications such as geopotential measurement.[22,23]

In this paper, we design and construct a power enhancement cavity to form an optical lattice for ytterbium(Yb)atoms.The waist diameter of the intra-cavity lattice light is 344µm,large enough to significantly reduce the atomic density and thereby the frequency shift due to atomic collision.Experimentally, we succeed in loading thousands of171Yb atoms from the magneto-optical trap(MOT)into the cavity-enhanced optical lattice with a trap depthUset in the range of 13Er-1400Er,whereEris the lattice photon recoil energy.The intracavity lattice power is increased by about 45 times.Such trap depths support accurate evaluation of the frequency shift of optical atomic clocks due to the lattice light.Moreover,based on interleaving measurements we evaluate the density shift of the Yb optical lattice clock to be-0.46(62) mHz, smaller compared to that of our first Yb optical lattice clock mainly due to a larger lattice waist.

2.Experimental setup

The schematic diagram of the optical clock based on Yb atoms trapped in a cavity-enhanced optical lattice is shown in Fig.1.Laser cooling and trapping Yb atoms are similar to our previous work.[24,25]In brief,171Yb atoms flying from an effusive oven are slowed down by absorbing an opposite propagation laser light at 399 nm,whose frequency is red-detuned from the1S0-1P1transition.The upper inset in Fig.1 shows the related energy levels of Yb atoms.Then the slowed atoms are trapped and cooled in a two-stage MOT,the first stage on the1S0-1P1transition and the second on the1S0-3P1transition.Consequently, nearly 105atoms with a temperature of about 15µK are ready for loading into an optical lattice.

The lattice laser light at 759 nm is from a Ti: sapphire continuous wave(c.w.) laser via a piece of polarization maintenance(PM)optical fiber.At the output of the PM fiber,it is reflected on a reflective Bragg grating (RBG) with a spectral bandwidth of 0.05 nm to reduce background spectra-induced Stark shift.[26]The diffraction efficiency of the RBG is～90%depending on the spatial mode of the input light.Then the diffracted light is phase-modulated at～50 MHz in an electrooptic modulator(EOM).The polarization of the light incident onto the EOM is aligned along the principal axis of the EO crystal to reduce undesired amplitude modulation,and an optical isolator(ISO)is placed after the EOM to prevent the cavity reflection light back into the EOM.A portion of the light after ISO is detected on a DC photo detector(PD2)to realize light power stabilization via adjusting the driving power of an acousto-optic modulator before the PM fiber(not shown in the figure).The transmitted laser light of the beam splitter(BS2)combines with laser light at 578 nm(clock laser on the transition of1S0-3P0).Two lenses are placed before BS2for mode matching of the 759 nm laser light with the lattice cavity.The polarizations of the 578 nm laser light and the lattice laser light are purified and matched on a polarizer (P2) before coupling into the lattice cavity.As shown in Fig.1,all the optics before P2are horizontally located on a platform.

In our previous system, 759 nm laser light with a power of 230 mW is focused, and it is retro-reflected by a curved mirror to build up an optical lattice,which has a trap depth of 80Erand a radius of 55µm.The intensity of the retro-reflected beam of the lattice is attenuated to 85%of the incident lattice light.In this work,a power enhancement lattice cavity is composed of two high-reflective mirrors, CM1and CM2, with a curvature of 250 mm separated by～20 cm.With the same number of atoms, a waist radius of 172 µm in the transverse plane enables a relatively low atomic density and thus a small density-dependent collisional shift.The cavity is formed vertically in order to lift degeneracy among different lattice sites and to suppress tunneling.[27]The curved mirrors of CM1and CM2are placed outside of the vacuum chamber.By measuring the cavity linewidth Δνcav(3.77 MHz), cavity reflectionRcav(as shown in the inset of Fig.1),cavity transmissionTcavof both an empty cavity and a cavity with vacuum windows placed inside the cavity, the transmissions of CM1and CM2are measured to beTin～1% andTout～0.015% at 759 nm,respectively.The lossLwof each vacuum chamber window is～0.5%at 759 nm.Thereby,the power-enhancement factor of the lattice cavity is estimated to be～41 according to[28]

whereF= 2π/Ltotis the finesse of the lattice cavity, andLtot=Tin+Tout+4Lwis the total loss of the cavity.In this work,F～199.

The cavity reflected laser light at 759 nm is steered onto PD1.By demodulating the AC signal from PD1with the driving signal of the EOM on a double balanced mixer, we obtain an error signal(the Pound-Drever-Hall signal[29])related to the cavity resonance detuning from the 759 nm laser frequency.Such an error signal is then used to tune the voltage applied to a piezo (PZT) attached to the output mirror of the lattice cavity, CM2.As long as the cavity is locked to the 759 nm laser light, the laser light can be resonant inside the cavity, and the cavity transmission light can be detected on PD3.In order to largely reduce the frequency shift due to the lattice light, the frequency of the 759 nm laser can be stabilized close to the magic wavelength via an optical frequency comb.[30]

3.Method and results

We load the atoms into the vertically-oriented onedimensional optical lattice.In order to obtain enough atoms trapped in the optical lattice,we set the initial trap depthUiin the range of 180Er-270Er.The lattice photon recoil energy is

wherehis the Planck constant,cis the speed of light,νlatis the lattice laser frequency, andmYbis the mass of the171Yb atom.By the end of the green MOT,we keep the lattice depth atUifor another 20 ms,and then we ramp the lattice depth to a desired value in 50 ms, as shown in Fig.2(a).By ramping the lattice power,we can load more atoms into the lattice,i.e.,nearly three times as that without ramping the lattice power.

Fig.2.(a)Experimental timing sequence of the Yb optical clock.(b)Motional sideband spectra at different trap depths,shown as the excitation fraction of the 3P0 state versus laser frequency detuned from the 1S0-3P0 clock transition.

After the Yb atoms are trapped in the lattice, we shine the clock laser light at 578 nm on the lattice-trapped atoms to excite the1S0-3P0transition.The transmissions of CM1and CM2are＞99% at 578 nm.The population in the3P0states is then measured in sequence using electron shelving detection.[31]Figure 2(b) shows the motional sideband spectra at different lattice depths.From the figure,we can deduce the trap depthU, longitudinal atomic temperature and vibrational state.[32]The longitudinal atomic temperature ranges from 1 µK to 25 µK whenUis set in the range of 13Er-1400Er.When the power of the 759 nm laser light incident onto the cavity is～600 mW, the trap depth approaches to 1400Er, the highest to date.Such a wide tuning range of the trap depth is suitable for experimental evaluation of the lattice-induced light shifts.[15,16]From the trap depthU, we can deduce the lattice power sensed by the atoms.Thereby the power-enhancement factor is measured to beG～45.For normal operation of a Yb atomic clock,the trap depth can be set to≤50Erin order to reduce the lattice light shift.Here we can trap～1000171Yb atoms when the trap depthUis lowered to 13Er.In that case,the power of the incident lattice light before the cavity is only～10 mW.

With enough171Yb atoms trapped in the power enhancement lattice cavity, we then probe the clock transition of Yb atoms with Rabi spectroscopy by stepping the 578 nm laser frequency.The atoms are prepared to either one of the two nuclear spin states of1S0by depleting the other spin state using a pumping light at 556 nm at a certain frequency and then decaying to the ground state.Three pairs of Helmholtz coils are employed to cancel the static stray magnetic field in three directions and to provide a bias magnetic fieldBto split the nuclear spin state degeneracy.The magnetic fieldBis oriented along with the polarization of the lattice light.When the atomic probe time is 200 ms and a single cycle time of 600 ms,a normalized excitation spectrum of the1S0(mF= +1/2)-3P0(mF= +1/2) clock transition with a spectral linewidth of～4.3 Hz (full width at half-maximum, FWHM) and an excitation rate of～0.8 at peak are observed, as shown in Fig.3(a),comparable to that without power enhancement lattice cavity.[25]The spectrum in Fig.3(a)is based on the171Yb atoms trapped in a lattice at a depth of 50Er.We also probe the clock transition of Yb atoms trapped in a lattice with a depth as low as 13Er,and similar Rabi spectra are observed.

Based on the above Rabi spectra, we use the measured excitation rate as a frequency discriminator to stabilize the frequency of the 578 nm laser to the atomic transition.To anticipate the frequency instability of the optical clock in a closed loop, we made an interleaved measurement,[25,33]which is close to a white noise model ofwhereτis the averaging time.

Fig.3.(a) Rabi spectrum of the 1S0 (mF =+1/2)-3P0 (mF =+1/2)clock transition of ytterbium atoms trapped in a cavity-enhanced optical lattice at a depth of 50Er.(b) Measured frequency difference Δ when the number of atoms is switched between 10Natom and Natom.(c) Fractional frequency instability of the interleaved measurement at two atomic densities.One-sigma error bars are shown.

By interleaving measurements at different atomic densities, the density shift is evaluated.[20,34]Assuming the same volume, the atomic density is proportional to the number of atoms.Here the number of atoms is set by changing the duration of the slower light at 399 nm during the first-stage MOT.Using this method,it does not impact the trapping conditions,and thus the density shift is proportional to the number of atoms.[21,35]When Yb atoms with an atomic temperature of 4 µK are trapped in the optical lattice at a trap depth ofU～50Er, we measure the frequency difference ofΔwhen the number of atoms is switched between 10NatomandNatomin each cycle,as shown in Fig.3(b),whereNatom～103is the number of atoms in normal operation.A single cycle time is 550 ms.This frequency difference ofΔis measured to be-4.1(5.6) mHz with the uncertainty determined by the standard deviation of the mean values of three sub-datasets(each sub-dataset is based on 4000 data points from Fig.3(b)).Figure 3(c) shows the instability of the frequency difference between two atomic densities, which can reach 1.5×10-17in an averaging time of 104s.Assuming the frequency shift is proportional to the atomic density,[20,35]in normal operation atNatom～103,the typical density shift is estimated to beΔ·Natom/(10Natom-Natom)=-0.46(62)mHz.

The measured density frequency shift in the cavity enhanced optical lattice is smaller than our previous result of-2.7(1.7) mHz, which is measured when the atoms are trapped in a normal lattice with a depth ofU～80Er, a lattice waist diameter of 110 µm and an atomic temperature of 0.8 µK.In both cases, the excitation rate of Yb atoms is～50%.Since the collision shift is insensitive to the trap depthUwhenU ＜100Er,[17]the smaller density shift measured in this paper is majorly due to a larger lattice waist in spite of a higher atomic temperature.

4.Conclusion

We report a lattice power-enhanced171Yb optical clock.The intra-cavity lattice power can be enhanced by about 45 times.In our current setup, we can set the trap depth of the lattice in the range of 13Er-1400Er, enabling us to accurately measure the frequency shift coefficients of the Yb optical clock due to lattice light in the next step.Meanwhile, it is possible to operate the Yb optical lattice clock in a low trap depth at 13Erfor a lower lattice light shift and a lower density shift, which will largely reduce the corresponding uncertainties down to～1×10-18.In addition,the clock system can be more compact with less power consumption and a smaller size of the lattice laser.

Acknowledgments

Project supported by the National Natural Science Foundation of China(Grant Nos.12334020 and 11927810)and the National Key Research and Development Program of China(Grant No.2022YFB3904001).