Coherent control and charge echo in a GaAs charge qubit

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1 LETTER Coherent control and charge echo in a GaAs charge qubit To cite this article: Bao-Chuan Wang et al 2017 EPL View the article online for updates and enhancements. Related content - Arbitrary phase shift of a semiconductor quantum dot charge qubit on a short time scale Gang Cao, Hai-Ou Li, Xiang-Xiang Song et al. - Time-dependent single-electron transport Toshimasa Fujisawa, Toshiaki Hayashi and Satoshi Sasaki - Qubits based on semiconductor quantum dots Xin Zhang, Hai-Ou Li, Ke Wang et al. This content was downloaded from IP address on 10/07/2018 at 09:40

2 March 2017 EPL, 117 (2017) doi: / /117/ Coherent control and charge echo in a GaAs charge qubit Bao-Chuan Wang, Bao-Bao Chen, Gang Cao (a), Hai-Ou Li, Ming Xiao and Guo-Ping Guo (b) Key Laboratory of Quantum Information, University of Science and Technology of China, Chinese Academy of Sciences - Hefei , China and Synergetic Innovation Center of Quantum Information & Quantum Physics, University of Science and Technology of China - Hefei , China received 7 February 2017; accepted in final form 12 April 2017 published online 9 May 2017 PACS PACS Kv Quantum dots Hk Coulomb blockade; single-electron tunneling Abstract In fulfilling the non-adiabatic requirement of pulse sequences, it is challenging to perform multi-pulse quantum control of a charge qubit. By optimizing our charge qubit and pulse parameters, we experimentally demonstrate the coherent control and echo process of a GaAs charge qubit. We firstly employed a single non-adiabatic voltage pulse to perform the Larmor oscillation experiment and determine the optimal σ x operation pulses. Then, we produced Ramsey fringes using two σ x = π/2 pulses and extracted the decoherence time T2 112 ps from the Ramsey fringes. More importantly, we successfully applied a charge echo pulse sequence to increase the extracted inhomogeneous dephasing time to 1360 ps. Our results show that the low-frequency noise is the important dephasing limiter of the coherence time of the charge qubit in the GaAs system. editor s choice Copyright c EPLA, 2017 Semiconductor quantum dots are a promising candidate for use in solid-state quantum computation and have attracted much attention in the last decade [1 4]. Using charge qubits in quantum dots is one encoding scheme that allows for quantum manipulation at fast operating speed [5 12]. Recently, research has demonstrated both silicon and GaAs charge qubits with strong coupling to the microwave cavity, which is an important milestone toward the development of quantum processors [13,14]. Thus, it is important to improve the coherent control and to increase the coherence time for charge qubits, whether using GaAs or silicon. However, a serious challenge for charge qubits is the rapid loss of coherence caused by interactions with the environment. Mitigating environment noise is an important way to prolong the coherence time [15,16]. Over the past decades, several pulse sequences have been developed to mitigate environment noise, including the echo and the extended dynamic decoupling pulse sequence [17 19]. Early experiments have been performed on semiconductor spin qubits, which have shown significant improvements in qubit coherence [20 24]. As for charge qubits, ultrafast operation brings many more technical difficulties. Until recently, coherent quantum control (a) gcao@ustc.edu.cn (corresponding author) (b) gpguo@ustc.edu.cn (corresponding author) has been realized and the decoherence time extended from 127 to 760 ps by using the echo pulse sequence, but only in silicon systems [11]. In the GaAs charge qubit, both the Larmor oscillation and the Ramsey interference have been realized, but it remains challenging to use a complicated echo sequence [9]. In addition to high-frequency technics, compared with silicon, the stronger piezoelectric effect and electron-phonon interaction in GaAs will theoretically lead to the relatively shorter coherence time which may be another challenge to perform charge echo sequences [16]. Simultaneously, in turn, the realization of the echo processes in a GaAs system will be helpful to clarify the roles played by the different decoherence mechanisms. In this paper, by optimizing the parameters of the qubit (inter-dot tunnel coupling and tunnel rates to leads) and pulse sequence (duration time and rise time), we experimentally demonstrated the coherent quantum control of a GaAs charge qubit. Both σ x and σ z rotations were realized. More importantly, we successfully performed an echo experiment in the GaAs charge qubit. The results of our experiment agree well with theoretical expectations and show significant improvement in the qubit coherence time to 1360 ps. We fabricated the present device on a GaAs/AlGaAs wafer, having the same structure as the one shown in p1

3 Bao-Chuan Wang et al. Fig. 1: (Colour online) (a) SEM image of the device structure used in the experiment. The dashed circles indicate the approximate positions of the quantum dots. I QP C was acquired by measuring the transconductance of the QPC channel. A voltage pulse was applied to gate U1. (b) Charge stability diagram of the defined charge qubit after applying one voltage pulse. (c) Schematic energy level structure of the charge qubit, with a minimal energy difference 2Δ at the anti-crossing point. (d) Coherent oscillations of the charge states while varying the pulse duration time t p. fig. 1(a). The surface metal gates, denoted as H1, H2, and U1 U5, form a typical double-quantum-dot structure. The other three gates, D1 D3, act as a highly sensitive quantum point contact (QPC). The sample was mounted in a dilution refrigerator with a base temperature of 30 mk. By applying a small modulation signal to gate U1 (typically 0.2 mv) and acquiring the QPC transconductance signal with a lock-in amplifier, we used standard lock-in modulation and detection techniques for the charge-sensing measurement. Figure 1(b) shows a charge stability diagram of the double quantum dot. Each quantum dot contains approximately five electrons, but we only need to consider the valence electrons for our charge qubit. We denote the charge occupation areas as (0, 0), (1, 0), (0, 1), and (1, 1), where (n, m) denotes the relative valence electron numbers in the left and right dots. The two basis states describing the logical charge qubit are defined as L and R, which correspond to charge occupation of the left dot and right dot: L =(1, 0) and R =(0, 1), respectively. These two states form a welldiscriminated two-level system. The Hamiltonian of this two-level system can be written as H = 1 2 εσ z +Δσ x, (1) where ε is the detuning and Δ is the tunnel coupling between the two dots. σ z and σ x are the Pauli matrices. Figure 1(c) shows a schematic energy level structure. The energy levels of the two basis states intersect at the zero detuning point and form an avoided crossing with a minimum energy splitting of 2Δ. In the experiment, we can adjust the detuning ε by sweeping the voltages applied to gates U1 and U5. Doing this will vary the energy difference between the two basis states. The tunnel coupling Δ can be tuned by using gate U3. In our experiment, we applied a fixed voltage of 430 mv to U3, which kept the tunnel coupling constant. An efficient way to manipulate a charge qubit is to use a non-adiabatic pulse sequence, as previous work has demonstrated well [5 7,12]. In the present work, we used the same technique to coherently drive our charge qubit. Figure 1(c) shows a schematic of the pulse sequence we p2

4 Coherent control and charge echo in a GaAs charge qubit Fig. 2: (Colour online) (a) Pulse sequence for the Ramsey fringe experiment and the corresponding evolution process represented on a Bloch sphere. (b) QPC transconductance response as a function of the delay time τ. The delay time starts at 200 ps to avoid an overlap of the two π/2 pulses. (c) Line cut from (b), marked by the black dashed line. The red solid line is the fit result, which gives T2 112 ps. (d) Simulation of the Ramsey fringes using an ideal pulse. used to realize Larmor precession. The pulse sequence was generated by an Agilent 81134a pulse generator and applied to gate U1 combined with the DC and small modulation signal via a bias tee, with a repetition rate of 40 MHz. We chose the pulse height ε p so we could initialize the charge qubit in state R, far from the anticrossing point ε = 0. Then, the pulse brought the qubit non-adiabatically to the anti-crossing point. At the anticrossing point, the qubit eigenstates are ( R ± L )/ 2. The qubit evolves according to the σ x rotation on the Bloch sphere. The precession frequency is determined by the energy difference of the two qubit states, which is 2Δ in this case. The precession continues until the pulse duration time t p is completed. Then, the pulse sequence takes the system away from the anti-crossing point, and finally the charge state is detected by the QPC. The interference fringes near the inter-dot transition line, as shown in fig. 1(b), are a signature of the nonadiabatic pulse operation. We swept the voltage applied to gates U1 and U5 along the direction of the arrow in fig. 1(b), simultaneously increasing the pulse duration time t p. Figure 1(d) shows the QPC transconductance response as a function of U1 and the pulse duration time t p, with the pulse height V p = 500 mv. The oscillations marked by the red dashed line in this figure correspond to the Larmor precession at the charge degeneracy point, which is robust because of the first order insensitive to detuning noise. We extracted a tunnel coupling of 2Δ/h 2.4 GHz from the oscillation frequency. These oscillations represent the evaluation of the qubit state probability between L and R, which corresponds to a σ x rotation in the qubit subspace, as schematically depicted on the Bloch sphere in fig. 1(c). To further explore the decoherence of the charge qubit, we used Ramsey interference. Figure 2(a) shows the Ramsey pulse sequence, excluding the measurement interval. Two single π/2 σ x rotations are separated by a free evolution time τ. We first prepared the qubit at positive detuning in state R, andthefirstσ x = π/2 pulse rotates the qubit into the x-y plane on the Bloch sphere. Then the qubit freely precesses about the z-axis in the x-y plane for a time τ, which can be regarded as a σ z rotation. The second σ x = π/2 pulse interrupts the free evolution and brings the qubit to the measurement interval. The measurement sequence recognizes the qubit states probability distribution. This should show distinct oscillations of the qubit state probability, attributed to the delay time between the two σ x rotations. As shown in fig. 2(b), the measured QPC transconductance exhibited clear oscillations as a function of the delay time τ and V U1, as expected, with t π/2 = 180 ps. We chose the delay time to start at 200 ps because a shorter delay time will overlap the two σ x pulse and generate a higher σ x pulse. The oscillation frequency in fig. 2(b) depends strongly on V U1, which is consistent with the theoretical expectation f = ε 2 +4Δ 2 /h. At the anti-crossing point p3

5 Bao-Chuan Wang et al. Fig. 3: (Colour online) (a) Pulse sequence for the charge echo experiment and the evolution process represented on the Bloch sphere. (b) QPC transconductance response as a function of δt. (I) (III) correspond to total evolution times of 400 ps, 1000 ps, and 1600 ps, respectively. (c) Echo amplitude dependence on the total evolution time t. The red solid line is a fit to the Gaussian form, which gives the inhomogeneous dephasing time T ps. (d) Simulation of the charge echo process. ε = 0, it will have a slowest oscillation frequency, which is equal to the Larmor frequency. A line cut near V U1 = mv is shown in fig. 2(c). The oscillation frequency is nearly 45 GHz, much larger than the Larmor frequency at the anti-crossing point. A fit to the form A exp[ (t t 0 ) 2 /T2 2]cos(ωt + θ) givest 2 = 112 ± 21 ps, which is of the same order as that reported in refs. [9] and [11]. We use the von Neumann equation approach to simulate the evolution of the two-level system under an ideal pulse sequence [9,12,15]. The π/2 pulse duration time in the ideal pulse sequence is chosen to be 100 ps. The pulse height is set as 180 uev which is consistent with the Ramsey oscillation frequency extracted from the experimental data. And the tunnel coupling 2Δ/h we used here is 2.4 GHz which is extracted from the Larmor oscillations. To account for the charge noise, we convolved each vertical sweep with a Gaussian function, exp[ (αvu1)2 2πσ 2 2σ 1 ], 2 ε ε with the width σ ε = 5 uev [9,12,15]. Figure 2(d) shows the simulated results of the same process. Comparing fig. 2(d) with fig. 2(b), the results of the simulation are in good agreement with the experimental data. The little mismatch may come from the waveform distortion since the pulse is too fast to be treated as an ideal square pulse. For example, the wavy background along the x-axis may be caused by superimposing the tailing pulses [12]. An effective approach to alleviate the influence of inhomogeneous dephasing is to use a charge echo pulse sequence, as schematically depicted in fig. 3(a). It initializes the qubit in state R at positive detuning. The first σ x = π/2 pulse brings the qubit to the anti-crossing point and rotates the Bloch vector to the x-y plane. Then the qubit undergoes a free evolution about the z-axisfor a time t/2 + δt. Aπ pulse interrupts the free evolution and flips the Bloch vector to its mirror image with respect to the x-z plane. After that, the qubit evolves freely about the z-axis for another time t/2 δt until the second σ x = π/2 pulse rotates the Bloch vector about the x-axis and brings the qubit to the measurement interval. Figure 3(b) shows the QPC transconductance response after applying the charge echo pulse sequence, with t π/2 = 180 ps, t π = 300 ps, and V p = 150 mv. The charge state should show oscillations as a function of δt near δt =0 for the charge echo. Figure 3(b) shows distinct oscillations, as expected. The oscillation patterns tend to show the strongest amplitude at δt = 0 for the best correction of the inhomogeneous dephasing. Figure 3(b) ((I) (III)) corresponds to the total evolution times of t = 400 ps, 1000 ps, and 1600 ps, respectively. The charge oscillation is much stronger in fig. 3(b) (I) than in fig. 3(b) ((II), (III)). In fig. 3(b) (III), the charge oscillation has nearly disappeared for the prominent dephasing during such a long evolution time. Using the dependence of the oscillation amplitude on the total free evolution time t, we extracted the inhomogeneous dephasing time. The detailed results of the echo amplitude dependence on evolution time t are shown in fig. 3(c). The data points in fig. 3(c) were obtained as follows: under each set of evolution time t in fig. 3(b), a line cut is extracted at V U1 = 684.0mV, where the pulse tip is around zero detuning. Each line cut shows the QPC transconductance oscillating as a function of δt. We chose the oscillating amplitude of each line cut p4

6 Coherent control and charge echo in a GaAs charge qubit around δt = 0 as the echo amplitude. The echo amplitude decays as the free evolution time t increases, with a characteristic dephasing time T 2. A fit to the Gaussian form A exp[ (t/t 2 ) 2 ]+C gives T 2 = 1360 ± 400 ps with the 95% confidence bounds and R-squared value , which is a significant improvement and nearly twice as long as that in the silicon system. The increase of coherence time indicates that the inhomogeneous dephasing can be effectively ameliorated by using the charge echo pulse sequence. Additionally, it indicates that low-frequencynoise is a crucial limiter of the charge qubit coherence in GaAs. We use the same method described in the Ramsey interference process to simulate the echo process with the 200 ps π pulse duration time. And the pulse height of the echo simulation is chosen to be 50 μev for consistence with our experiment. Figure 3(d) is a simulation of the charge echo process with various free evolution times t. These results agree well with the experiment. The oscillation frequency of the charge qubit is in the order of GHz. The ultrafast evolution imposes very strict technical requirements on pulse quality. It is a serious challenge especially for the multi-pulse operations. In previous work, a similar pulse sequence was used to implement the charge echo experiment in GaAs charge qubits [9]. However, no echo signals have been observed. As suggested in ref. [9], the most important thing is that the voltage pulse must be non-adiabatic, otherwise the qubit would simply remain in the ground state. We achieved this goal based on two main improvements: First, we improved our high-frequency circuits so that the pulse rise time is much shorter than that of early experiments [9,11,15]. This can be inferred from the Larmor oscillations diagrams. Here, our pulses reach the maximum value at t p 160 ps which is much shorter than that of 400 ps. Second, we tuned the tunnel coupling to be 2Δ/h 2.4 GHz, compared with 4 GHz in the previous work. The small tunnel coupling not only enhances the non-adiabatic evolution but also improves the precision of quantum operations σ x = π/2 andπ for the longer duration time. At the same time, we used a smaller pulse amplitude in the echo experiment than that in the Larmor and Ramsey experiments. This could reduce the echo oscillation frequency and increase the visibility of the echo signals from QPC measurement [9]. In conclusion, we experimentally demonstrated the quantum control of a GaAs charge qubit using nonadiabatic pulse sequence. The Larmor oscillation and Ramsey interference exhibited a good performance for the σ x and σ z rotations of the charge qubit, respectively. Moreover, we successfully ameliorated the inhomogeneous dephasing and increased the qubit coherence time by applying the charge echo pulse sequences. This is the first time an experiment has produced an echo in a GaAs charge qubit. From the relative similarity of our result to that in the silicon system, we infer that, presently, the most important factor limiting charge qubit coherence is the low-frequency charge noise. Therefore, effectively reducing the charge noise in the gate electrode and measurement electronic circuit may significantly prolong the charge qubit coherence time in future investigations. This work was supported by the National Key R&D Program (Grant No. 2016YFA ), the National Natural Science Foundation of China (Grants No , No , No , No , and No ), the Strategic Priority Research Program (B) of the Chinese Academy of Sciences (Grant No. XDB ), and the Fundamental Research Fund for the Central Universities. 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