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实验上展示了钇铁石榴石(YIG)晶体小球中磁振子与超导量子比特的驱动缀饰态之间的相干强耦合, 磁振子的加入使得在超导量子比特中形成了双重缀饰态. 实验中一个钇铁石榴石晶体小球与一个超导量子比特同时放置在三维谐振腔中, 分别通过磁偶极相互作用和电偶极相互作用与谐振腔中的本征场(
$\mathrm{TE_{102}}$ 模式)耦合, 并通过腔模作为媒介实现两者之间的有效相干强耦合. 给超导量子比特施加一个共振的微波驱动并改变驱动强度, 测得耦合系统能级劈裂随驱动强度的变化, 并理论上利用粒子-空穴对与玻色场耦合的模型做了计算. 在大部分的驱动强度范围内实验结果都与理论计算结果符合得较好, 表明驱动下的比特-磁振子耦合系统可以用来模拟粒子-空穴对称对与玻色场的耦合系统. 本文使用的混合量子系统为模拟玻色子与费米子的混合系统提供了一个新途径.We experimentally demonstrate the strong coupling between the ferromagnetic magnons in an yttrium-iron-garnet (YIG) sphere and the drive-field-induced dressed states of a superconducting qubit, which gives rise to the double dressing of the superconducting qubit. The YIG sphere and the superconducting qubit are embedded in a microwave cavity, and are coupled to the magnetic and electrical fields of the cavity$\mathrm{TE}_{102}$ mode, respectively. The effective coupling between them is mediated by the virtual cavity photons of cavity$\mathrm{TE}_{102}$ mode. Our experimental results indicate that as the power for driving the qubit increases, an additional split of the qubit-magnon polariton occurs. These supplemental splittings indicate a double-dressed state. We theoretically analyze the experimental results by using a particle-hole symmetric model. The theoretical results fit the experimental observations well in a broad range of drive-field power parameters, revealing that the driven qubit-magnon hybrid quantum system can be used to emulate a particle-hole symmetric pair coupled to a bosonic mode. Our hybrid quantum system holds great promise for quantum simulations of composite quasiparticles consisting of fermions and bosons.-
Keywords:
- superconducting qubit /
- magnon /
- coherent coupling /
- quantum simulation
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图 1 量子比特与磁振子耦合系统示意图 (a) 超导量子比特与磁振子耦合系统示意图, 其中量子比特与YIG小球同时放置在三维谐振腔中. 谐振腔由无氧铜腔和铝腔两部分组成, YIG小球放置在谐振腔无氧铜材质的半腔内使得磁场可以穿透, 量子比特放置在铝的半腔内以得到更好的磁屏蔽效果. YIG小球放置在谐振腔TE102模式磁场的波腹位置以获得两者之间更大的耦合强度, 同时量子比特放置在TE102模式电场的波腹. (b) 腔TE102和TE103模式电磁场分布的示意图. 上半图为腔TE102模式的电场分布, 下半图左侧为腔TE102模式的磁场分布, 右侧为腔TE103模式的电场分布. 可以看到, YIG小球和超导量子比特芯片分别放置在腔TE102模式磁场最大值和TE102模式电场较大值位置, 考虑到需要通过TE103模式读取比特, 并没有把芯片放置在TE102模式电场最大处. (c) 谐振腔TE102的透射谱. 改变外加静磁场强度来改变YIG小球中基泰尔模磁振子的共振频率, 图中展示的是磁振子与腔TE102 模式近共振附近的谱线, 可以看到两者相干耦合产生的反交叉劈裂
Fig. 1. Schematic of qubit-magnon hybrid system in a rectranglar 3D microwave cavity: (a) A small YIG sphere is placed in cavity made of oxygen-free copper at the magnetic-field antinode of the cavity mode TE102. The qubit is mounted in the part of the cavity made of aluminium near the antinode of cavity TE102 mode. (b) Electrical and magnetic field distribution of cavity TE102 and TE103 mode. The upper half figure shows the electric field distribution of cavity TE102 mode, the left of lower half shows the magnetic field distribution of cavity TE102 mode, TE103 mode electric field distribution is shown on the right-hand side. As shown in figure, the YIG sphere and the qubit chip are placed near the antinodes of cavity TE103 magnetic field and TE102 electric field, respectively. (c) Transmission spectrum of the cavity when the Kittel mode of magnons in the YIG sphere is magnetically tuned to be near resonance with the cavity TE102 mode
图 2 量子比特与磁振子的耦合 (a) 量子比特与磁振子耦合系统的能级结构, 图中只考虑了基泰尔模磁振子的单量子态和基态. 调节磁振子的谐振频率使得磁振子的能级差与比特能级差对上, 能级
$ |g, 1\rangle $ 与$ |e, 0\rangle $ 简并并出现劈裂, 耦合强度即真空拉比劈裂 2gqm, 进一步给比特施加微波驱动Ωd, 劈裂的两个能级进一步劈裂成四个能级. (b) 量子比特-磁振子相干耦合系统的真空拉比劈裂. 实验上改变磁振子的外加磁场把两者频率调到近共振, 对超导量子比特加驱动微波, 同时用谐振腔TE103模式读取腔的传输谱来反映比特的变化Fig. 2. Coherent coupling between qubit and the magnon: (a) Energy levels of qubit-magnon system with only the vacuum and single-magnon states involved for the Kittle mode. If we adjusting the magnetic field to set magnon Kittle mode frequency resonance with the qubit,
$ |g, 1\rangle $ and$ |e, 0\rangle $ degenerates, the coupling between$ |g, 1\rangle $ and$ |e, 0\rangle $ induces the vacuum Rabi splitting 2gqm. If we apply a microwave drive with amplitude Ωd to qubit, the degenerated levels further split into 4 levels. (b) Vacuum Rabi splitting of the qubit-magnon system measured via the transmission spectrum of the cavity by both tuning the static magnetic field and scanning the frequency of the excitation field. The porbe field is applied in resonance with the cavity TE103 mode图 3 量子比特-磁振子耦合系统能级劈裂随外加微波场驱动强度的变化, 其中
$ \delta_{\rm{q}}=\delta_{\rm{m}}=0 $ . 使用驱动微波去激发比特, 同时用一个与读取腔${\rm{TE}}_{103}$ 共振的微波进行色散读取. 驱动微波的功率分别是(a)$0.04\;{\text{μW}}$ , (b)$0.06\;{\text{μW}}$ , (c)$0.1\;{\text{μW}}$ , (d)$0.16\;{\text{μW}}$ , (e)$0.4\;{\text{μW}}$ , (f)$0.63\;{\text{μW}}$ , (g)$1\;{\text{μW}}$ , (h)$1.6\;{\text{μW}}$ Fig. 3. Dispersive readout of the hybridized normal modes of the driven qubit-magnon system. An excitation field is tuned to excite the hybridized normal modes and a probe field is applied in resonance with the cavity mode
${\rm{TE}}_{103}$ . The power of the microwave field to drive the superconducting qubit is tuned to be (a)$0.04\;{\text{μW}}$ , (b)$0.06\;{\text{μW}}$ , (c)$0.1\;{\text{μW}}$ , (d)$0.16\;{\text{μW}}$ , (e)$0.4\;{\text{μW}}$ , (f)$0.63\;{\text{μW}}$ , (g)$1\;{\text{μW}}$ , (h)$1.6\;{\text{μW}}$ , respectively图 4 量子比特-磁振子耦合系统频率劈裂随外加微波场驱动强度变化的拟合. 上半图数据(绿色圆点和绿线)是耦合模式1和模式4 (见正文)之间能级差随驱动功率
$ P_{\rm{d }}$ 的变化. 下半图数据(橙色圆点和橙线)是耦合模式3和模式2能级差随驱动功率$ P_{\rm{d}} $ 的变化. 使用(5)式进行拟合, 其中$ |\tilde{g}_{{\rm{qm}}}|=|g_{{\rm{qm}}}| $ ,$ n_{\rm{m}}=0 $ , 以及$\varOmega_{\rm{d}}=k\sqrt{P_{\rm{d}}}$ , 这里$k= $ $103{\text{ MHz/}{\text{μW}}^{1/2}}$ Fig. 4. Fitting the experimental data of the frequency splitting between hybridized normal modes 1 and 4 (3 and 2) versus the drive power
$ P_{\rm{d}} $ . To fit the data, we use Eq. (5), where$ |\tilde{g}_{{\rm{qm}}}|=|g_{{\rm{qm}}}| $ ,$ n_{\rm{m}}=0 $ , and$\varOmega_{\rm{d}}=k\sqrt{P_{\rm{d}}}$ with$k=103{\text{ MHz/}{\text{μW}}^{1/2}}$ -
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