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Abstract
Divacancy in silicon carbide has become an important solid-state system for quantum metrologies. To make it more beneficial for practical applications, we realize a fiber-coupled divacancy-based magnetometer and thermometer simultaneously. First, we realize an efficient coupling between the divacancy in a silicon carbide slice with a multimode fiber. Then the optimization of the power broadening in optically detected magnetic resonance (ODMR) of divacancy is performed to obtain a higher sensing sensitivity of 3.9 μT/Hz1/2. We then use it to detect the strength of an external magnetic field. Finally, we use the Ramsey methods to realize a temperature sensing with a sensitivity of 163.2 mK/Hz1/2. The experiments demonstrate that the compact fiber-coupled divacancy quantum sensor can be used for multiple practical quantum sensing.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
In recent years, solid-state spin systems have become important platforms for various quantum metrologies due to their excellent optical and spin properties [1,2]. Particularly, the nitrogen-vacancy (NV) center in diamond as a key representative of solid-state spin systems has been widely used in various quantum metrologies with both high sensitivity and high spatial resolution [2]. In order to realize the practical application of NV center-based quantum sensors, several schemes have been applied to compact the laboratory confocal systems [3–8]. Among those, the fiber-integrated method has been one of the promising schemes [3–7]. Recently, portable and distributed NV center-based fiber magnetometers have been realized [5,6]. Besides, fiber-coupled NV center-based thermometry has also been realized and applied to sensing the thermal activation of the transient in a living cell [9]. However, the lack of mature fabrication technologies and the high expense of the diamond limit its widespread practical applications [10–12]. Moreover, the excitation laser at 532 $nm$ and the fluorescence at 600-800 $nm$ of the NV center make some optical damages to the living cell and limit its transmission distance in fiber [13].
In order to solve these problems, in recent years, spin qubits in silicon carbide (SiC) have attracted increasing attention [10–12,14]. SiC is a widely used semiconductor, with mature micro-fabrication, inch-scale-growth, and device engineering technologies [10–12], which is convenient for the application of the SiC-based quantum sensing. There are three representative spin qubits in SiC including silicon vacancy [12], divacancy [10,11,14], and NV centers [15]. And their spin signals can be read out through optically detected magnetic resonance (ODMR) methods. Over the past decade, divacancy has become a promising candidate for various quantum technologies [10,11,14]. Both the excitation laser and photoluminescence (PL) spectra of divacancy are in the infrared range, which will cause less absorption and auto-fluorescence in the living cells and have a long transmitting distance in fiber network [10,11,13,16]. Moreover, it has a long coherence time ($ms$) [11] which can be extended to 5 $s$ using dynamical decoupling methods combined with isotopically purified SiC [17]. Most recently, coherent manipulation of single divacancy with a high readout contrast at room temperature has also been demonstrated [13]. These excellent properties have been applied in quantum photonics [18], quantum information process [17], spin-photon interface [19], and quantum sensing [20]. Great efforts have been made to apply the divacancy to various quantum sensing such as magnetic field [21], temperature [14,22], electric field [20], and strain [23]. However, all those experiments are performed using macroscopic laboratory setups [17–23]. In order to apply it in practical environments, both the total setup and the sensor size need to be reduced, optimized, and integrated. The integration of the multifunction divacancy-based quantum sensor is still a challenge.
In this study, we realize the fiber-integrated divacancy-based magnetometer and thermometer simultaneously. First, we paste a tiny slice of SiC sample with divacancy on the multimode fiber facet and we use a homemade copper-wire coil to act as a microwave antenna, then move the coil close to the fiber facet to control the spin of the divacancy. In order to improve the sensing sensitivity, we optimize the divacancy ODMR spectra through different microwave and laser powers. On this basis, we use the magnetometer to detect the strength of the c-axis external magnetic field. Finally, we realize high-sensitivity temperature sensing using the Ramsey methods. The results prove that the fiber-coupled divacancy quantum sensor can be used in the practical magnetic field and temperature sensing.
2. Experiments and results
The experimental setup is depicted in Fig. 1(a). The homemade optical and microwave systems are developed to excite and control the spin state of the divacancy, respectively. A 914 $nm$ laser is used to excite divacancy efficiently. After reflected by a dichroic mirror (DM), the laser is collected to a multimode fiber to excite the pasted tiny sample on the other end of the multimode fiber. Then the fluorescence signals of the divacancy are also transmitted through the same fiber and filtered by a 1000 nm long-pass (LP) filter. Finally, the fluorescence signals are collected by a photoreceiver (Femto, OE-200-IN1). The pulse sequences generated by a pulse generator (PBESR-PRO-500, Spincore) are sent to an acoustic optical modulator (AOM) and a microwave (MW) switch to control laser and MW sequences, respectively. MW signals generated by a MW generator are amplified and connected to a homemade copper coil to be transmitted to the sample. To obtain a sample with a high density of divacancy, 30 $keV$ nitrogen ions with a dose of 1 $\times$ 10$^{14}$/$cm^{2}$ are implanted in a bulk high-purity 4H-SiC epitaxy layer sample surface. Then the sample is annealed at 1050 $^{\circ }$C for 2 h. [24]. And the overall density of divacancy is about 1.3 $\times$ 10$^{3}$ / $\mu m^{2}$. To efficiently couple with fiber, we polish it to a thickness of about 50 $\mu m$. Figure 1(b) shows the optical image of a pasted sample (around 100$\times$100 $\mu m^{2}$) on a fiber tip. The homemade microwave antenna is placed close to the sample to control the spin state of divacancy. The standard lock-in method is used to detect the spin signal of the divacancy [10,14,15,22].
Fig. 1. Experimental setup. (a) Home-made optical and microwave system. After reflected by a dichroic mirror, the 914 $nm$ laser is collected by a lens to a multimode fiber which transmits the laser to pump the sample on the fiber end face. Then the fluorescence is collected through the same path reverse and collected by photoreceiver (Femto). The microwave generator sends MW signals to the sample through a copper coil. Heater and electromagnet are placed close to the sample to change environmental temperature and magnetic field, respectively. (b) Optical image of the SiC sample and copper coils. (c) Saturation curve of the ensemble of fiber-coupled divacancy defects. The red line is the fitting of the data.
Efficient coupling of the divacancy to the multimode fiber is the basis of the experiment. First, we measure the saturation curve, and the results are presented in Fig. 1(c). The counts increase with the increasing laser power. The maximum count is about 760 $Mcps$ under the laser power of 230 $mW$. We use the function $I(P)=I_{s}/(P_{0}/P+1)$ to fit the data, where $P$ is the laser power, $P_{0}$ is the saturation laser power and $I_{s}$ stands for the saturation count of the sample [15,21]. As fitted, the saturation laser power $P_{0}$ is about 1050 $mW$, and the maximum count $I_{s}$ can reach about 4120 $Mcps$.
The ODMR is the cornerstone of various quantum sensing applications [2]. The optimized ODMR is vital for high-sensitivity magnetic field and temperature sensing [14,21,22]. The ODMR contrast and full width at half maximum (FWHM) of the divacancy are also affected by the power broadening from the laser and MW [21]. To reach the highest sensitivity, the influence of MW and laser powers on ODMR spectra should be studied. A 50 $G$ c-axis external magnetic field is applied to the fiber-coupled SiC sample. The right branch of PL6 ODMR Frequency (at the magnetic field of 50 G) is picked to study the influence of laser and MW power. We then fit the measured ODMR spectra using the Lorentzian function to obtain the ODMR contrast and FWHM at different laser and MW powers. We first study the effect of the MW power on the divacancy ODMR. As seen from Fig. 2(a) and 2(b), both the ODMR contrast and the FWHM increase as the MW power increases from -0.5 $dBm$ to 22 $dBm$, which is consistent with previous results [21]. The sensitivity of the magnetometer can be approximately written as:
where $h$, $g$, $\mu _B$ represent Plank constant, g factor, and Bhor magneton, respectively. $\Delta \nu$ represents the FWHM of ODMR, while $C$ and $R$ are ODMR contrast and fluorescence count, respectively. As shown in Fig. 2(c), the divacancy magnetic field sensing sensitivity increases with the increasing MW power. The maximum sensitivity can be optimized to 3.9 $\mu T / Hz^{1/2}$, which is almost the same as the previous optimized sensitivity measured in the confocal system [21].Fig. 2. Optimization of the divacancy ODMR spectra. (a) and (b) Divacancy ODMR contrast and FWHM as a function of MW power. (c) Divacancy magnetic field sensitivity as a function of MW power. (d) Divacancy ODMR contrast with respect to laser power, which shows a decrease with increasing laser powers. (e) Divacancy ODMR FWHM as a function of laser power, which is approximately constant with varied laser powers. (f) Divacancy magnetic field sensitivity as a function of laser power.
Fig. 3. Magnetic field sensing. (a) Two ODMR spectra under different magnetic fields, and the red lines are the Lorentz fitting of the data. The splitting of PL6 under a non-zero magnetic field is shown. (b) Resonant frequencies of the two splitting PL6 under different c-axis magnetic fields, and the red lines are the theoretical calculations.
We then investigate the ODMR spectra with the laser power. Figure 2(d) presents the ODMR contrast with respect to laser power from 1 $mW$ to 240 $mW$ with a constant MW power of 15 $dBm$. The results show that the ODMR contrast decreases as laser power goes up. Figure 2(e) shows that the divacancy FWHM of the ODMR stays constant at about 10 $MHz$ with laser power varies from 1 $mW$ to 240 $mW$, which is consistent with the previous divacancy and silicon-vacancy results [21,25]. Figure 2(f) shows the measured divacancy magnetic field sensitivity as a function of laser power. The sensitivity rapidly increases with the laser power increasing from 1 $mW$ to 120 $mW$ and then decreases slowly after the laser power exceeds 120 $mW$. The maximum magnetic field sensing sensitivity reaches 4.5 $\mu T/Hz^{1/2}$ at the laser power and MW power of 120 $mW$ and 15 $dBm$, respectively. The results prove the high sensitivity of the fiber-coupled divacancy.
After optimizing the ODMR spectra, we then apply the fiber-coupled divacancy (PL6) magnetometer to detect an external magnetic field. As presented in Fig. 3(a), three kinds of divacancy defects are shown in this period of MW frequency including divacancy PL5, PL6, and PL7. The PL6 is a c-axis divacancy defect, in our experiment, its direction is perpendicular to the sample surface. The ODMR of PL6 will split into two frequencies under an external magnetic field (50 $G$) due to the Zeeman splitting as shown in Fig. 3(a), and they are picked to detect the external magnetic field. Figure 3(b) summarizes the the two branches of PL6 ODMR resonant frequencies as a function of the c-axis magnetic field from 0 $G$ to 110 $G$. Both resonant frequencies vary linearly with the magnetic field with slopes of 2.8 $MHz/G$ and −2.8 $MHz/G$, respectively, which is consistent with theoretical calculations. The magnetic sensing sensitivity can be further increased through higher fluorescence collection efficiency methods [3] and pulsed ODMR methods [26]
In addition to magnetic field sensing, by taking advantage of the temperature-dependent zero-field-splitting (ZFS) of PL5 divacancy, the fiber-coupled divacancy multifunction quantum sensor can be also applied to detect the temperature in a 100 $\mu m$-level spatial resolution. A metal ceramic heater (HT24S2, Thorlabs) is used to change the local environment temperature. A resistive temperature sensor (TH100PT, Thorlabs) is pasted on the fiber close to the sample to measure the sample temperature. By focusing on the right branch of PL5, we scan the ODMR spectrum over a wide temperature range from 304.2 $K$ to 373.9 $K$ without external magnetic fields. As presented in Fig. 4(a), the ZFS shifts from 1374.3 $MHz$ to 1369.7 $MHz$ in the temperature range of 314.1 $K$ to 361.5 $K$. As is shown in Fig. 4(b), the ZFS decreases linearly with temperature from 304.2 $K$ to 373.9 $K$. By the linear fitting, the slope of resonance frequency versus temperature is about −101 $\pm$ 3 $kHz/K$, which agrees with the previous results [14].
Fig. 4. Temperature sensing. PL5 divacancy ODMR spectra under different temperatures. (b) The ZFS of PL5 as a function of temperature, the red line is the linear fitting. (c) Rabi oscillation, where the oscillation frequency is fitted to be about 5.6 MHz. (d) and (e) Ramsey measurement at 304.6 $K$ and 312.1 $K$, respectively. (f) Ramsey oscillation frequencies increase linearly with the temperature increasing from 304 $K$ to 318 $K$.
To further increase the temperature sensing sensitivity, Ramsey fringes are applied to detect the local temperature [14,22]. In the experiment, both the initialization and read-out laser pulse lengths are 5 $\mu s$ [15]. After getting the ODMR resonant frequency, we first measure the Rabi oscillation (Fig. 4(c)), obtaining an oscillation frequency of about 5.6 $MHz$. Figure 4(d) shows the measurement of the Ramsey at 304.6 $K$, and the red line is the fitting using an exponentially decaying cosine function:
where $a$, $n$, $b$ and $c$ are fitting parameters, $f$ is the oscillation frequency and $T^{\ast }_{2}$ is the dephasing time [14,21,27]. Inferred from the fitting, the dephasing time $T^{\ast }_{2}$ is about 0.42 $\mu s$ and the oscillation frequency $f$ is about 5858 $\pm$ 17 $kHz$. The sensitivity of the fiber-coupled thermometer is expressed as:3. Conclusion
There are three prospective ways to improve the sensitivity. First, the density of divacancy can be further increased by electron irradiation [11]. Second, the excitation fluorescence collection efficiency can be further improved with methods like micro-concave mirror [28], surface coating with silver reflective film [29], tapered fiber [3] and so on. Moreover, some methods can be applied to increase the sensitivity like the pulsed ODMR methods [26] for magnetic field sensing and thermal dynamical decoupling methods [27] for temperature sensing which will increase the coherence time of Ramsey.
In conclusion, we experimentally prove a fiber-coupled silicon carbide divacancy-based magnetometer and thermometer. First, we realize an efficient coupling between the divacancy sample with a fiber. Furthermore, a homemade microwave antenna is moved close to the fiber tip to transmit the microwave signals at the same time. We then minimize the power broadening of the laser and microwave and get a magnetic field sensing sensitivity of 3.9 $\mu T/Hz^{1/2}$. The fiber-coupled divacancy magnetometer is applied to detect an external magnetic field. Finally, we also realize the temperature sensing using the Ramsey methods with a sensitivity of 163 $mK/Hz^{1/2}$. The results give the basis for the fiber-coupled divacancy-based magnetometer and thermometer for reality application.
Funding
National Natural Science Foundation of China (61905233, 11975221, 11874361); Science Specialty Program of Sichuan University (2020SCUNL210); Youth Innovation Promotion Association of the Chinese Academy of Sciences (2021446); CAS Innovation Grant (CXJJ-19-B08).
Disclosures
The authors have no conflicts of interest to disclose.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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