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Abstract
We present a matter wave gyroscope with a Sagnac area of 5.92 cm2, achieving a short-term sensitivity of 167 nrad/s/Hz1/2. The atom interferometry gyroscope is driven by a π/2 − π − π − π/2 Raman pulse sequence based on an atom fountain with a parabolic trajectory. The phase-locked laser beams for Raman transitions partly propagate outside of the vacuum chamber and expose to the air when passing through the two arms of the vacuum chamber. This configuration leads to the tilt of the laser’s wave-front and suffers the fluctuation of air density. The impacts on both the fringe contrast and long-term stability are experimentally investigated in detail, and effective schemes are developed to improve the performance of our atom gyroscope. The method presented here could be useful for developing large atom interferometry facilities with separated vacuum chambers.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Atom interferometers (AI) are widely used as quantum inertial sensors, such as gravimeters [1–9], gravity gradiometers [10–14], and tiltmeters [15–18]. Especially, Sagnac gyroscopes based on atom interferometry have been highly concerned for the reason of high-potential sensitivity. The atom interferometry gyroscope (AIG) was firstly demonstrated with thermal beams [19], and the AIG with thermal Cs beams has reached up to high sensitivity soon [20,21]. Since people can manipulate the cold atoms more precisely and make it possible to miniaturize the setup, nowadays, the light-pulse AIG based on the atom fountain develops rapidly. There are mainly two types of light-pulse AIGs at present, including three Raman pulses sequence $\pi /2- \pi - \pi /2$ [22–24] with two identical counterpropagating atomic clouds and four Raman pulses sequence $\pi /2- \pi - \pi - \pi /2$ [25–28] with a single atomic cloud, both configurations are used to eliminate the constant acceleration phase of the Mach-Zehnder atom interferometer [27]. Particularly, in the configuration of the four-pulse AIG, the phase shift induced by rotation only depends on the effective wave vector, the local gravitational acceleration and the interrogation time. These three terms can be determined with high accuracy that makes the rotation-induced phase shift much more stable. Moreover, the rotation phase shift of the four-pulse AIG is in direct proportion to $T^{3}$, the rotation-induced phase shift increases faster with the interrogation time than that of the three-pulse AIG. These advantages make the four-pulse AIG reached record sensitivity of $30\ \textrm{nrad/s/Hz}^{1/2}$ in the high-precision rotation measurements [26].
In our AIG, cold atoms are coherently manipulated by two-photon stimulated Raman transitions [29]. Similar to the most large-scale AIGs, more than one laser beam are needed to obtain a large Sagnac area. To ensure that two arms of the atom interferometer recombine within the coherence length of the cold atoms, we have to adjust the effective wave vectors of the Raman beams (i.e. the effective wave-fronts of the Raman beams) in every atom-light interaction zone to be parallel. The method to align the manipulation laser beams is introduced for the three-pulse Mach-Zehnder Sagnac interferometer in Ref. [30]. Reference [28,31] describe the procedure of the Raman beams’ parallelism adjustment for the four-pulse AIG. In our case, the AIG, that based on a parabolic trajectory with long baseline, uses four Raman pulses sequence ($\pi /2- \pi - \pi - \pi /2$). Different from the configuration of vertical trajectory [28], as shown in Fig. 1(b), for the $4^{th}$ pulse, comparing with the $1^{st}$ pulse, the $\pi /2$ Raman beam propagates outside the vacuum chamber. This resulted in not only the changing of the Raman beam’s direction, but also the increasing of the Raman beam’s optical path. We theoretically analyze and experimentally investigate these effects in detail: By inserting the compensation glass plates, we correct the direction change of the $\pi /2$ Raman beam; we also carefully calculate the extra phase shift and correct the phase fluctuation of the AIG via the air density measurement system. With these methods, we demonstrate a sensitive AIG with a Sagnac area of $5.92\ {\textrm{cm}^2}$, the short-term sensitivity of the AIG reaches up to $167\ \textrm{nrad/s/Hz}^{1/2}$, and the stability reaches about $30\ \textrm{nrad/s}$ at $40\ \textrm{s}$ integration time. The long-term stability of the AIG is improved nearly one order of magnitude after the air density correction at $2500\ \textrm{s}$ integration time.
Fig. 1. (a) The diagram of the four-pulse AIG. We built the large area AIG with a $\pi /2- \pi - \pi - \pi /2$ Raman-pulse sequence separated by $T+\Delta T$, $2T$ and $T-\Delta T$ respectively. The total interrogation time of the AIG is $4T=546\ \rm {ms}$, and we introduce the $\Delta T=200\ {\mu \textrm{s}}$ to suppress the other two atom interferometers due to the imperfect $\pi$ Raman pulses in a four-pulse interferometer [25]. (b) The experimental setup of the four-pulse AIG. The size of the AIG vacuum chamber is about $1.9\times 0.6\times 1.4\ \textrm{m}^3$, and the configuration of the trapping beams, the velocity-selection Raman beams along z and y direction, the $\pi /2$ Raman beam, the $\pi$ Raman beam and the detection beams are also shown in the figure. The auxiliary Raman beam and the compensation glass plates are used to compensate the wave-front tilt as show in Sec. 3.
The contents are as follows: Section 2 presents the principle and experimental setup of the AIG based on a parabolic trajectory. In the AIG, the $\pi /2$ Raman beam propagates outside the vacuum chamber between the $1^{st}$ pulse and the $4^{th}$ pulse, as a consequence, (i) The direction of the Raman beam changes since that the two sides of the vacuum windows and the two ends of the air region are not paralleled. (ii) The Raman beam’s optical path increases since the refractive indexes of the windows and the air are greater than 1, leads to an extra Raman laser phase shift. To solve these problems, we at first show the method to compensate the Raman beam’s wave-front tilt in Sec. 3. Then we analyse the air density influence of the AIG in detail in Sec. 4. Finally, we conclude this work in Sec. 5.
2. Principle and experimental setup
The principle of the four-pulse AIG is illustrated in Fig. 1(a). A $\pi /2- \pi - \pi - \pi /2$ Raman-pulse sequence interacts with the atoms successively, as a consequence, the atomic wave packet is coherently split, reflected, reflected again, and finally recombined. We get the total phase difference $\phi _{\textrm{tot}}$ of the two arms of the atom interferometer by measuring the mean transition probability $P$ as:
where $C$ is the contrast of the interferometry fringe. The total phase shift $\phi _{\textrm{tot}}$ consists of the rotation phase $\phi _{\textrm{rot}}$, the laser phase $\phi _{\textrm{L}}$, and the other phase $\phi _{\textrm{oth}}$ caused by the gravity gradient, the magnetic field and so on, and can be expressed as:In the Earth gravity field, the cold atoms are launched along a parabolic trajectory. The horizontal $\pi /2- \pi - \pi - \pi /2$ pulses sequence leads to a rotation-sensitive Sagnac area, and we can derive the phase shift induced by rotation as [27]:
The laser phase $\phi _{\textrm{L}}$ arises from the atom-light interaction processes, and can be written as:
where ${\phi _{\textrm {i}}} = {\vec k_{\textrm{eff}}}{\vec r_{\textrm {i}}} + {\phi _{\textrm {0,i}}}\left ( {i = 1,2,3,4} \right )$ is the laser phase for the $i\rm {th}$ pulse, ${\vec r_{\textrm {i}}}$ is the atom position when the $i\rm {th}$ Raman pulse is switched on, and ${\phi _{\textrm {0,i}}}$ is the initial phase of the $i\rm {th}$ Raman pulse.The schematic of the AIG is briefly shown in Fig. 1(b). The ultra-high vacuum chamber shapes as "$\pi$" configuration for the parabolic atomic trajectory, and consists of the two-dimensional magneto-optical trap (2D-MOT), the three-dimensional magneto-optical trap (3D-MOT), the interference region, and the detection zone. The $^{87} \rm {Rb}$ atoms are pre-cooled in the 2D-MOT, and loaded into the 3D-MOT. In our AIG, about $3\times 10^{9}$ atoms are trapped within $350\ \rm {ms}$. We then launch the atoms along a parabolic trajectory using the moving molasses technique with the atomic cloud temperature of $2.5\ \rm {\mu k}$. The initial velocity of the atomic cloud is about $4.27\ \rm {m/s}$ at an angle of $20.7\ ^{\circ }$ with respect to the vertical direction.
We shut down the repumping beam of the 3D-MOT with a time delay of $10\ \rm {ms}$ after the moving molasses, as a result, the launched cold atoms are distributed in the $\left | {{5^2}{S_{\textrm {1/2}}},F = 2} \right \rangle$ state. Then, we prepare atoms in the magnetic-insensitive hyperfine state $\left | {{5^2}{S_{\textrm {1/2}}},F = 1,{m_{\textrm {F}}} = 0} \right \rangle$ through a microwave pulse and an $\rm {F=2}$ blow away pulse. A $\pi$ Raman pulse with Doppler sensitive configuration is switched on with pulse duration of $100\ \rm {\mu s}$ to select atoms in a narrow region of velocity distribution in y direction, and an $\rm {F=1}$ blow away pulse removes the remaining atoms in $\rm {F=1}$. Furthermore, a z-direction Raman pulse with a duration of $50\ \rm {\mu s}$ and an $\rm {F=2}$ blow away pulse are switched on in turn to obtain the velocity selection in z direction. Finally, we obtain about $10^{4}$ cold atoms in the $\left | {{5^2}{S_{\textrm {1/2}}},F = 1,{m_{\textrm{F}}} = 0} \right \rangle$ state.
The cold atoms arrive at the interference zone at $129.06\ \rm {ms}$ after launch. After that, a $\pi /2- \pi - \pi - \pi /2$ Raman-pulse sequence manipulates the atomic wave packet successively. The center of the AIG time sequence coincides with the moment when the cold atoms arrive at the apex of the parabolic trajectory ($402.06\ \rm {ms}$ after launch). There are two Raman beams to construct the large-area AIG. The two Raman beams are separated by $274\ \rm {mm}$ in vertical direction to ensure the four-pulse interferometer has an interrogation time of $4T=546\ \textrm{ms}$. The Raman beams are composed of two phase-locked lasers [4] with a total power of $80\ \rm {mW}$ respectively, and the $1/e^2$ diameters are about $26\ \rm {mm}$, ensuring the $\pi /2$ Raman pulse duration of $30\ \rm {\mu s}$. The Raman beams are reflected by two mirrors to obtain the counterpropagating configuration. We mount a seismometer (CMG-3SEP) next to the mirrors to monitor the vibration noise which is used for the vibration correction [32] during the experiment. After a total atom flying time of $750\ \rm {ms}$, we obtain the transition probability $P$ and fringes through a normalized fluorescence detection method, the phase shift of the AIG can be extracted from the fringes. The cycle time of the experiment is $1.2\ \rm {s}$.
3. Compensating the tilt of the Raman beam’s wave-front
To obtain the large AIG, we have to adjust the Raman beams to be parallel in each interaction area. As shown in Fig. 1(b), the $\pi /2$ Raman beam passes through the two arms of the vacuum chamber, there are two vacuum windows and air between the $1^{st}$ and the $4^{th}$ interaction zones in the light path of the $\pi /2$ Raman beam. We draw the light path of the $\pi /2$ Raman beam in Fig. 2, for the purpose of simplicity, we focus on the y-z plane and only the optical components which affect the wave-front are given. As shown in Fig. 2, both the two sides of the vacuum windows and the two ends of the air region are not paralleled. After the $\pi /2$ Raman beam passing through these windows and air region, the direction of propagation changes, resulted in the unparallel wave-fronts of the $1^{st}$ and the $4^{th}$ pulses. Assume that the $\pi /2$ Raman beam propagates in the horizontal plane in the $1^{st}$ interaction zone, after passing through the first vacuum window, the angular shift of the $\pi /2$ Raman beam $\triangle \beta _1$ can be derived as:
Fig. 2. The light path of the $\pi /2$ Raman beam in the y-z plane. The direction of the $\pi /2$ Raman beam in the $4^{th}$ zone changes $\triangle \beta _2$ compared to the direction in the $1^{st}$ zone because that both the two sides of the vacuum windows and the two ends of the air region are not paralleled.
As discussed above, Figs. 3(a-i) and (b-i) show the change of the $\pi /2$ Raman beam’s wave-front while passing through the vacuum windows and air. To compensate the tilt of the wave-front, we insert several compensation glass plates between the vacuum windows as shown in Fig. 3(c-i). The compensation glass plates are made of quartz, and the parallelism of the compensation glass plate was precisely measured with a precision of $1\ \rm {\mu rad}$. By choosing several appropriate glass plates and rotating the glass plates to the right angle, the wave-fronts of the $1^{st}$ and $4^{th}$ pulses could be adjusted to be parallel. The direction of the effective wave vectors in every interaction zone, perpendicular to the wave-front, are also shown in Fig. 3.
Fig. 3. Principle for compensating the tilt of the $\pi /2$ Raman beam’s wave-front. (a-i,b-i) The MZ-R (MZ-L) atom interferometer built by the auxiliary Raman beam and the $\pi /2$ Raman beam is used to align the wave-front of the auxiliary Raman beam and the $4^{th}$ ($1^{st}$) pulse. We also show the light path of the $\pi /2$ Raman beam and the evolution of the wave-front of the $1^{st}$ and the $4^{th}$ pulses. (a-ii,b-ii) The fringe patterns of the MZ-R atom interferometer and the MZ-L atom interferometer for different $\beta _1$, $\beta _1$ is the relative tilt angle of the $\pi /2$ Raman beam mirror and $\beta _1=0\ \rm {\mu rad}$ when the effective wave vector of the $4^{th}$ pulse is parallel to that of the auxiliary Raman beam. The contrasts of the AIs decrease rapidly when the effective wave vectors in the different interaction zones are misaligned. The contrasts of the MZ-R AI and the MZ-L AI don’t reach the maximums simultaneously, and the angular difference (about $600\ \rm {\mu rad}$), namely the tilt difference of the wave-front of the $1^{st}$ pulse and the $4^{th}$ pulse is caused by the vacuum windows and air. (c-i) The light path of the $\pi /2$ Raman beam and the evolution of the wave-front of the $1^{st}$ and $4^{th}$ pulses with wave-front compensation. The wave-front of the $1^{st}$ pulse is corrected by the compensation glass plates, and is adjusted parallel to the wave-front of the $4^{th}$ pulse. (c-ii) The fringe patterns of the MZ-R AI and the MZ-L AI when we compensate the tilt of the wave-front completely.
In order to check whether the glass plates compensate the tilt of the wave-front perfectly, we introduce the auxiliary Raman beam. The auxiliary Raman beam is used as a reference beam, and we align the wave-fronts of the $1^{st}$ and the $4^{th}$ pulses parallel to the wave-front of the auxiliary Raman beam respectively by introducing other atom interferometers. The auxiliary Raman beam is configured similar to the $\pi /2$ and the $\pi$ Raman beams, and overlaps with the atomic cloud at moments of $311.06\ \rm {ms}$ and $493.06\ \rm {ms}$ after atom launching. The procedure to compensate the $\pi /2$ Raman beam wave-front is illustrated as follow: (i) We adjust the auxiliary Raman beam to propagate in the horizontal plane with the method in the atom interferometry tiltmeter [16], the auxiliary Raman beam tilt angle with respect to the horizontal plane $\beta _{\textrm{a}}$ is adjusted with a precise of $5\ \rm {\mu rad}$. (ii) Shown in the Fig. 3(a-i), the right-side Mach-Zehnder atom interferometer (MZ-R AI) is used to adjust the wave-front of the $4^{th}$ pulse parallel to the wave-front of the auxiliary Raman beam. The MZ-R AI shares the second $\pi /2$ pulse with the $4^{th}$ pulse of AIG. The effective wave vector of the $4^{th}$ pulse can be aligned with respect to the effective wave vector of the auxiliary Raman beam by optimizing the contrast of the MZ-R AI. As shown in the Fig. 3(a-ii), the fringes appear only if when the auxiliary Raman beam and the $\pi /2$ Raman beam are well-aligned, and we record the mirror angle of the $\pi /2$ Raman beam ${\beta _{\textrm{R}}},{\gamma _{\textrm{R}}}$ in z and x direction respectively when the contrast of the MZ-R AI reaches the maximum. The interference pattern of the left-side Mach-Zehnder interferometer (MZ-L AI) doesn’t appear during the adjustment, which is caused by the tilt of the wave-front when the $\pi /2$ Raman beam passing through these windows and the air region. (iii) The MZ-L AI is used to adjust the wave-front of the $1^{st}$ pulse parallel to that of the auxiliary Raman beam as shown in Fig. 3(b-i). Similar to the step (ii), we record the mirror angle ${\beta _{\textrm{L}}},{\gamma _{\textrm{L}}}$ in z and x direction respectively when the contrast of the fringe of MZ-L AI reaches the maximum as shown in Fig. 3(b-ii). (iv) The angular differences $\left ( {{\beta _{\textrm{R}}} - {\beta _{\textrm{L}}}} \right ),\left ( {{\gamma _{\textrm{R}}} - {\gamma _{\textrm{L}}}} \right )$ are the angle between wave vectors ${\vec k_{\textrm{eff,1R}}}$ (${\vec k_{\textrm{eff,1L}}}$) and ${\vec k_{\textrm{eff,4R}}}$ (${\vec k_{\textrm{eff,4L}}}$) in z and x direction respectively. These differences are caused by the vacuum windows and air. To compensate the angular difference, several compensation glass plates with total parallelism of ${{\left ( {{\beta _{\textrm{R}}} - {\beta _{\textrm{L}}}} \right )} \mathord {\left / {\vphantom {{\left ( {{\beta _{\textrm{R}}} - {\beta _{\textrm{L}}}} \right )} {\left ( {{{{n_{\textrm{win}}}} \mathord {\left / {\vphantom {{{n_{\textrm{win}}}} {{n_{\textrm{air}}}}}} \right. } {{n_{\textrm{air}}}}} - 1} \right )}}} \right. } {\left ( {{{{n_{\textrm{win}}}} \mathord {\left / {\vphantom {{{n_{\textrm{win}}}} {{n_{\textrm{air}}}}}} \right. } {{n_{\textrm{air}}}}} - 1} \right )}}$ in z direction and ${{\left ( {{\gamma _{\textrm{R}}} - {\gamma _{\textrm{L}}}} \right )} \mathord {\left / {\vphantom {{\left ( {{\gamma _{\textrm{R}}} - {\gamma _{\textrm{L}}}} \right )} {\left ( {{{{n_{\textrm{win}}}} \mathord {\left / {\vphantom {{{n_{\textrm{win}}}} {{n_{\textrm{air}}}}}} \right. } {{n_{\textrm{air}}}}} - 1} \right )}}} \right. } {\left ( {{{{n_{\textrm{win}}}} \mathord {\left / {\vphantom {{{n_{\textrm{win}}}} {{n_{\textrm{air}}}}}} \right. } {{n_{\textrm{air}}}}} - 1} \right )}}$ in x direction are inserted between the vacuum windows. The compensation glass plates give the wave-front of the $\pi /2$ Raman beam an angular shift of $- \left ( {{\beta _{\textrm{R}}} - {\beta _{\textrm{L}}}} \right ), - \left ( {{\gamma _{\textrm{R}}} - {\gamma _{\textrm{L}}}} \right )$ in z and x direction respectively, balance the angular difference $\left ( {{\beta _{\textrm{R}}} - {\beta _{\textrm{L}}}} \right ),\left ( {{\gamma _{\textrm{R}}} - {\gamma _{\textrm{L}}}} \right )$ completely. (v) We resume the $\pi /2$ Raman beam mirror back to the same position as step (ii) as shown in Fig. 3(c-i), and then all of the ${\vec k_{\textrm{eff,1C}}}$, the ${\vec k_{\textrm{eff,4C}}}$, the ${\vec k_{\textrm{eff,1L}}}$, the ${\vec k_{\textrm {eff,4R}}}$ and the ${\vec k_{\textrm{eff,a}}}$ are adjusted to horizontal. Ultimately, the contrasts of the MZ-R AI and the MZ-L AI reach the maximums simultaneously as shown in Fig. 3(c-ii), indicating we compensate the tilt of the Raman beam’s wave-front completely, and the wave-front compensation precision by optimizing the contrast is $20\ \rm {\mu rad}$. Furthermore, we seal the light path of the $\pi /2$ Raman beam by a heat insulation cover to reduce the air flow and the temperature fluctuation.
To estimate the alignment precision, we both theoretically calculate and experimentally verify the angular influence on the contrasts of the three types of atom interferometers. Using the method from Ref. [30], the expressions of the contrast of the MZ-L AI and the MZ-R AI in z direction can be derived as:
As shown in Fig. 4, we find good agreement of the measured contrast to theoretically calculation. The $1/e^2$ Gaussian widths of the contrasts of the MZ-L AI and the MZ-R AI are about $184\ \rm {\mu rad}$ and $84\ \rm {\mu rad}$ respectively, showing that the precision of the compensation method can reach up to the level of ten micror adian by maximizing the contrast. Then, by the means described in Ref. [28], we align the $\pi$ Raman beam with respect to the $\pi /2$ Raman beam, and the contrast of the AIG as a function of the angular difference of the $\pi$ Raman beam and the $\pi /2$ Raman beam is also shown in Fig. 4. The $1/e^2$ Gaussian width of the contrast of the AIG is calculated as ${1 \mathord {\left / {\vphantom {1 {\left ( {2{k_{\textrm{eff}}}{\sigma _{\textrm{vz}}}T} \right )}}} \right. } {\left ( {2{k_{\textrm{eff}}}{\sigma _{\textrm{vz}}}T} \right )}} = 154\ \rm {\mu rad}$, coincides with the result of the experiments, the error mainly arises from the adjustment resolution of the mirror.
Fig. 4. The contrasts of the MZ-L AI (black squares), the MZ-R AI (red circles) as a function of the relative angle of the $\pi /2$ Raman beam in z direction, and the contrast of the AIG (blue triangles) as a function of the relative angle of the $\pi /2$ Raman beam in z direction. The solid lines are the theoretical curves respectively.
Finally, we obtain the fringe of the AIG as shown in Fig. 5, the dominant limitation of the AIG’s sensitivity is the vibration noise, a post-correction method [33] is used here to suppress the vibration noise, leading an improvement from $450\ \textrm{nrad/s/Hz}^{1/2}$ to $300\ \textrm{nrad/s/Hz}^{1/2}$ as shown in Fig. 6. To reach a higher sample rate and higher sensitivity, we adopt the fringe lock technique, and use the linear vibration correction to suppress the vibration noise [33], making the gyroscope be able to reach a sensitivity around $167\ \textrm{nrad/s/Hz}^{1/2}$. Figure 6 displays the Allan deviations of the AIG by fringe locking, the improvement of the rotation measurement by our AIG after air density correction is also shown.
Fig. 5. The fringe pattern of the AIG with vibration correction. The solid line is the sinusoidal fit of the population of the F=2 state.
Fig. 6. The Allan deviations of the AIG. The Allan deviations by fringe fitting without and with vibration correction are displayed as open pink squares and open red circles respectively. The Allan deviations from fringe lock are also shown as full up blue and full down black triangle, corresponding to the results before and after air density correction.
In our large-area AIG, the sensitivity is mainly limited by the Raman beam phase noise after vibration correction, it is estimated at the level of $120\ \textrm{nrad/s/Hz}^{1/2}$. The detection noise ${\sigma _{\textrm{P}}}$ is measured to be $0.7\%$ per shot, contributing an equivalent noise level of $73\ \textrm{nrad/s/Hz}^{1/2}$ for rotation measurements. The rotation noise of the AIG, evaluated by two seismometers and the rotation transfer function, can be derived as $42\ \textrm{nrad/s/Hz}^{1/2}$. The long-term stability of the AIG is limited by the fluctuation of the air density detailed in the follow.
4. Air density effect on the AIG
Comparing with the $1^{st}$ pulse, there is an extra optical path for the $4^{th}$ pulse. The phase difference of the $\phi _1$ and the $\phi _4$ can be expressed as:
The extra Raman laser phase shift derives from the extra optical path since the refractive indexes of the windows and the air are greater than 1. The lengths of the windows ${l_{\textrm{win}}}$ and the length of the air ${l_{\textrm{air}}}$ shrink when temperature decreases, the refractive index of the windows ${n_{\textrm{win}}}$ decreases with temperature increasing [34], and the refractive index of the air ${n_{\textrm{air}}}$ changes as the air density changes. We have monitored the temperature and the air density by the thermometer and the air density measurement system, and estimated the extra phase shift ${\phi _{\textrm{extra}}}$ from the Equ. 11. From the calculation, the biggest factor that restricts the stability of the AIG is the fluctuation of the air density. The relationship between the refractive index and the air density can be written as [35,36]:
To decrease the influence of the air density fluctuation, a heat insulation cover was fixed between the first and the second pulse window (the air pressure inside the cover is still atmospheric). This cover can prevent the air convection and reduce the air density fluctuation, but without preventing the Raman laser beam. The short term sensitivity is improved with the cover, but the long-term stability is still limited by the air density fluctuation, probably caused by the air leak of the cover or the deformation of the cover when the air pressure changes.
Shown in the Fig. 7(a), the phase shift of the AIG is recorded for about 16 hours. We also monitor the fluctuation of the air density, and we find that the change of the phase shift and the fluctuation of the air density are in good agreement. The phase shift shows strong correlation with the fluctuation of air density, as can be seen in Fig. 7(c), the Pearson’s correlation coefficient between the phase shift and the fluctuation of air density is 0.99. The result shows that the stability of the total phase shift of the AIG is mainly limited by the air density, agrees with the theoretical calculation. The residual phase shift after deducing the influence of the air density is also shown in Fig. 7(b), and the Allan deviation of the residual phase is shown in Fig. 6. The stability of the residual rotation rate is about $45\ \textrm{nrad/s}$ at $2500\ \textrm{s}$, improved nearly one order of magnitude comparing to without air density correction. The stability of the residual rotation signal is possibly limited by the fluctuation of the temperature, which leads to a changes of the lengths of the refractive index of the windows, the windows or the length of the air (Eq. (11)). The stability of the AIG in the time range of $10\ \textrm{s}$ to $300\ \textrm{s}$ is worse after the air density correction, possibly due to the finite precision of the air density measurement system ($0.001\ \rm {kg/m^3}$).
Fig. 7. The influence of the air density on the AIG. (a) The phase shift extracted by the AIG (blue point) and the variation of the air density (black line) record by an air density measurement system (National Institute of Metrology, China, ADMS1306). The linear correlation of the phase shift and the air density is shown in the inset (c). (b) The residual phase shift after deducing the effect of the air density.
5. Conclusion
In conclusion, we report an atom interferometry gyroscope with a Sagnac area of $5.92\ \textrm {cm}^2$ based on a large-scale parabolic trajectory. The AIG is constructed with two Raman beams, and the $\pi /2$ Raman beam passes through the two arms of the vacuum chamber and propagates in the air, resulted in a tilt of the wave-front and an extra optical path. During the experiment, we use several glass plates to compensate the direction difference between the $1^{st}$ and the $4^{th}$ pulses. Since the $\pi /2$ Raman beam propagates through the windows and the air, the extra optical path leads an extra phase shift, and we show the analytical approach of the air density fluctuation effect. This work could be conducive to build the discrete atom interferometers with signal laser beam such as in [12] or one atom interferometer with separated Raman beam windows such as in [30].
Another solution to eliminate the influence of the air density is enclose the $\pi /2$ Raman beam light path in a low-vacuum chamber as in [12], the low-vacuum environment decreases the extra phase shift as well as the fluctuation of the extra phase shift. What’s more, to thoroughly solve the $\pi /2$ Raman beam propagation problem, we can install a vacuum tube to connect the two arms of the vacuum chamber directly. As a result, the $\pi /2$ Raman beam propagates in vacuum between the $1^{st}$ and the $4^{th}$ pulses, which can thoroughly eliminate both the propagation direction change and the extra phase shift. This will help us to improve the performance of the AIG in the future.
Funding
National Natural Science Foundation of China (11625417, 11727809, 11922404, 91636219, 91736311).
Disclosures
The authors declare no conflicts of interest.
References
1. A. Peters, K. Y. Chung, and S. Chu, “High-precision gravity measurements using atom interferometry,” Metrologia 38(1), 25–61 (2001). [CrossRef]
2. M. Hauth, C. Freier, V. Schkolnik, A. Senger, M. Schmidt, and A. Peters, “First gravity measurements using the mobile atom interferometer gain,” Appl. Phys. B 113(1), 49–55 (2013). [CrossRef]
3. R. Karcher, A. Imanaliev, S. Merlet, and F. P. Dos Santos, “Improving the accuracy of atom interferometers with ultracold sources,” New J. Phys. 20(11), 113041 (2018). [CrossRef]
4. Z.-K. Hu, B.-L. Sun, X.-C. Duan, M.-K. Zhou, L.-L. Chen, S. Zhan, Q.-Z. Zhang, and J. Luo, “Demonstration of an ultrahigh-sensitivity atom-interferometry absolute gravimeter,” Phys. Rev. A 88(4), 043610 (2013). [CrossRef]
5. K. S. Hardman, P. B. Wigley, P. J. Everitt, P. Manju, C. C. Kuhn, and N. P. Robins, “Time-of-flight detection of ultra-cold atoms using resonant frequency modulation imaging,” Opt. Lett. 41(11), 2505–2508 (2016). [CrossRef]
6. S. Abend, M. Gebbe, M. Gersemann, H. Ahlers, H. Müntinga, E. Giese, N. Gaaloul, C. Schubert, C. Lämmerzahl, W. Ertmer, W. P. Schleich, and E. M. Rasel, “Atom-chip fountain gravimeter,” Phys. Rev. Lett. 117(20), 203003 (2016). [CrossRef]
7. S. M. Dickerson, J. M. Hogan, A. Sugarbaker, D. M. Johnson, and M. A. Kasevich, “Multiaxis inertial sensing with long-time point source atom interferometry,” Phys. Rev. Lett. 111(8), 083001 (2013). [CrossRef]
8. J. Fang, J. G. Lu, X. Chen, H. R. Zhou, L. Zhou, J. Q. Zhong, J. Wang, and M. S. Zhan, “Realization of a compact one-seed laser system for atom interferometer-based gravimeters,” Opt. Express 26(2), 1586–1596 (2018). [CrossRef]
9. X. Wu, Z. Pagel, B. S. Malek, T. H. Nguyen, F. Zi, D. S. Scheirer, and H. Müller, “Gravity surveys using a mobile atom interferometer,” Sci. Adv. 5(9), eaax0800 (2019). [CrossRef]
10. N. Yu, J. M. Kohel, J. R. Kellogg, and L. Maleki, “Development of an atom-interferometer gravity gradiometer for gravity measurement from space,” Appl. Phys. B 84(4), 647–652 (2006). [CrossRef]
11. F. Sorrentino, Q. Bodart, L. Cacciapuoti, Y. H. Lien, M. Prevedelli, G. Rosi, L. Salvi, and G. M. Tino, “Sensitivity limits of a raman atom interferometer as a gravity gradiometer,” Phys. Rev. A 89(2), 023607 (2014). [CrossRef]
12. G. W. Biedermann, X. Wu, L. Deslauriers, S. Roy, C. Mahadeswaraswamy, and M. A. Kasevich, “Testing gravity with cold-atom interferometers,” Phys. Rev. A 91(3), 033629 (2015). [CrossRef]
13. X.-C. Duan, M.-K. Zhou, D.-K. Mao, H.-B. Yao, X.-B. Deng, J. Luo, and Z.-K. Hu, “Operating an atom-interferometry-based gravity gradiometer by the dual-fringe-locking method,” Phys. Rev. A 90(2), 023617 (2014). [CrossRef]
14. P. Asenbaum, C. Overstreet, T. Kovachy, D. D. Brown, J. M. Hogan, and M. A. Kasevich, “Phase shift in an atom interferometer due to spacetime curvature across its wave function,” Phys. Rev. Lett. 118(18), 183602 (2017). [CrossRef]
15. H. Ahlers, H. Müntinga, A. Wenzlawski, M. Krutzik, G. Tackmann, S. Abend, N. Gaaloul, E. Giese, A. Roura, R. Kuhl, C. Lämmerzahl, A. Peters, P. Windpassinger, K. Sengstock, W. P. Schleich, W. Ertmer, and E. M. Rasel, “Double bragg interferometry,” Phys. Rev. Lett. 116(17), 173601 (2016). [CrossRef]
16. W.-J. Xu, M.-K. Zhou, M.-M. Zhao, K. Zhang, and Z.-K. Hu, “Quantum tiltmeter with atom interferometry,” Phys. Rev. A 96(6), 063606 (2017). [CrossRef]
17. X. Wu, F. Zi, J. Dudley, R. J. Bilotta, P. Canoza, and H. Müller, “Multiaxis atom interferometry with a single-diode laser and a pyramidal magneto-optical trap,” Optica 4(12), 1545–1551 (2017). [CrossRef]
18. I. Perrin, J. Bernard, Y. Bidel, N. Zahzam, C. Blanchard, A. Bresson, and M. Cadoret, “Zero-velocity atom interferometry using a retroreflected frequency-chirped laser,” Phys. Rev. A 100(5), 053618 (2019). [CrossRef]
19. F. Riehle, T. Kisters, A. Witte, J. Helmcke, and C. J. Bordé, “Optical ramsey spectroscopy in a rotating frame: Sagnac effect in a matter-wave interferometer,” Phys. Rev. Lett. 67(2), 177–180 (1991). [CrossRef]
20. T. L. Gustavson, A. Landragin, and M. A. Kasevich, “Rotation sensing with a dual atom-interferometer sagnac gyroscope,” Classical Quantum Gravity 17(12), 2385–2398 (2000). [CrossRef]
21. D. S. Durfee, Y. K. Shaham, and M. A. Kasevich, “Long-term stability of an area-reversible atom-interferometer sagnac gyroscope,” Phys. Rev. Lett. 97(24), 240801 (2006). [CrossRef]
22. A. V. Rakholia, H. J. McGuinness, and G. W. Biedermann, “Dual-axis high-data-rate atom interferometer via cold ensemble exchange,” Phys. Rev. Appl. 2(5), 054012 (2014). [CrossRef]
23. P. Berg, S. Abend, G. Tackmann, C. Schubert, E. Giese, W. P. Schleich, F. A. Narducci, W. Ertmer, and E. M. Rasel, “Composite-light-pulse technique for high-precision atom interferometry,” Phys. Rev. Lett. 114(6), 063002 (2015). [CrossRef]
24. Z. W. Yao, S. B. Lu, R. B. Li, J. Luo, J. Wang, and M. S. Zhan, “Calibration of atomic trajectories in a large-area dual-atom-interferometer gyroscope,” Phys. Rev. A 97(1), 013620 (2018). [CrossRef]
25. J. K. Stockton, K. Takase, and M. A. Kasevich, “Absolute geodetic rotation measurement using atom interferometry,” Phys. Rev. Lett. 107(13), 133001 (2011). [CrossRef]
26. D. Savoie, M. Altorio, B. Fang, L. A. Sidorenkov, R. Geiger, and A. Landragin, “Interleaved atom interferometry for high-sensitivity inertial measurements,” Sci. Adv. 4(12), eaau7948 (2018). [CrossRef]
27. B. Canuel, F. Leduc, D. Holleville, A. Gauguet, J. Fils, A. Virdis, A. Clairon, N. Dimarcq, C. J. Bordé, A. Landragin, and P. Bouyer, “Six-axis inertial sensor using cold-atom interferometry,” Phys. Rev. Lett. 97(1), 010402 (2006). [CrossRef]
28. I. Dutta, D. Savoie, B. Fang, B. Venon, C. G. Alzar, R. Geiger, and A. Landragin, “Continuous cold-atom inertial sensor with 1 nrad/sec rotation stability,” Phys. Rev. Lett. 116(18), 183003 (2016). [CrossRef]
29. D. S. Weiss, B. C. Young, and S. Chu, “Precision measurement of $\hbar /m_{\textrm{cs}}$ based on photon recoil using laser-cooled atoms and atomic interferometry,” Appl. Phys. B 59(3), 217–256 (1994). [CrossRef]
30. G. Tackmann, P. Berg, C. Schubert, S. Abend, M. Gilowski, W. Ertmer, and E. M. Rasel, “Self-alignment of a compact large-area atomic sagnac interferometer,” New J. Phys. 14(1), 015002 (2012). [CrossRef]
31. M. Altorio, L. A. Sidorenkov, R. Gautier, D. Savoie, A. Landragin, and R. Geiger, “Accurate trajectory alignment in cold-atom interferometers with separated laser beams,” Phys. Rev. A 101(3), 033606 (2020). [CrossRef]
32. B. Barrett, L. Antoni-Micollier, L. Chichet, B. Battelier, P. A. Gominet, A. Bertoldi, P. Bouyer, and A. Landragin, “Correlative methods for dual-species quantum tests of the weak equivalence principle,” New J. Phys. 17(8), 085010 (2015). [CrossRef]
33. S. Merlet, J. L. Gouët, Q. Bodart, A. Clairon, A. Landragin, F. P. Dos Santos, and P. Rouchon, “Operating an atom interferometer beyond its linear range,” Metrologia 46(1), 87–94 (2009). [CrossRef]
34. T. Toyoda and M. Yabe, “The temperature dependence of the refractive indices of fused silica and crystal quartz,” J. Phys. D: Appl. Phys. 16(5), L97–L100 (1983). [CrossRef]
35. H. Fang, A. Picard, and P. Juncar, “A heterodyne refractometer for air index of refraction and air density measurements,” Rev. Sci. Instrum. 73(4), 1934–1938 (2002). [CrossRef]
36. A. Picard and H. Fang, “Three methods of determining the density of moist air during mass comparisons,” Metrologia 39(1), 31–40 (2002). [CrossRef]
