Experimental demonstration of switching entangled photons based on the Rydberg blockade effect

TL;DR

This paper demonstrates a single-photon optical switch using Rydberg blockade to control entangled photons, advancing quantum information processing by enabling interaction control between Rydberg atoms and entangled photon pairs.

Contribution

It provides the first experimental demonstration of switching entangled photons based on the Rydberg blockade effect, showing effective control of single photons in quantum networks.

Findings

Over 50% photon blocking efficiency achieved

Switching depends on principal quantum number and gate photon number

Effective single-photon switch demonstrated with Rydberg blockade

Abstract

The long-range interaction between Rydberg-excited atoms endows a medium with large optical nonlinearity. Here, we demonstrate an optical switch to operate on a single photon from an entangled photon pair under a Rydberg electromagnetically induced transparency configuration. With the presence of the Rydberg blockade effect, we switch on a gate field to make the atomic medium nontransparent thereby absorbing the single photon emitted from another atomic ensemble via the spontaneous four-wave mixing process. In contrast to the case without a gate field, more than 50% of the photons sent to the switch are blocked, and finally achieve an effective single-photon switch. There are on average 1-2 gate photons per effective blockade sphere in one gate pulse. This switching effect on a single entangled photon depends on the principal quantum number and the photon number of the gate field. Our experimental progress is significant in the quantum information process especially in controlling the interaction between Rydberg atoms and entangled photon pairs.

Equations

$$|\psi ⟩=(|H_{s1}⟩|V_{s2}⟩+e^{i\theta }|V_{s1}⟩|H_{s2}⟩)/\sqrt{2}$$

$${\mathrm{C}}_{\mathrm{switch}}=\frac{\mathrm{C}{\mathrm{C}}_{\mathrm{EIT}}-\mathrm{C}{\mathrm{C}}_{\mathrm{gate}}}{\mathrm{C}{\mathrm{C}}_{\mathrm{EIT}}},$$

Full text

Keywords: Rydberg blockade, entangled photon, quantum switch

Pacs numbers: 32.80.Rm, 42.50.Gy, 42.50.Ct, 42.50.Nn

1. Introduction

In analogy to classical electronic counterparts, quantum switches are regarded as basic building blocks for quantum circuits and networks Cirac et al. (1997); O’brien et al. (2009); Caulfield and Dolev (2010); Wang et al. (2018). Switching states in the full-quantum regime where single particles control a quantum qubit or entanglement from another system may enable further applications in quantum information science, such as in quantum computing Saffman et al. (2010), distributed quantum information processing Kimble (2008); Cui et al. (2019); Xie (2020), and metrology Komar et al. (2014). Many efforts have been done towards constructing a prototype; examples include a micro-resonator coupled with a single atom O’Shea et al. (2013), cold atoms trapped in a microscopic hollow fiber Bajcsy et al. (2009), cold atoms coupled to a cavity Chen et al. (2013), strongly coupled quantum cavity-dots Volz et al. (2012), and single dye molecules Hwang et al. (2009).

The strong interaction offered by Rydberg-excited atoms shifts the energy levels of the surrounding atoms dramatically and suppresses all further excitation of these neighboring atoms. This interaction between cold atoms gives rise to excitation blockade Comparat and Pillet (2010); Jaksch et al. (2000); Lukin et al. (2001); Tong et al. (2004); Singer et al. (2004); Urban et al. (2009); Gaëtan et al. (2009), multipartite entanglement Heidemann et al. (2007); Zeiher et al. (2015); Labuhn et al. (2016); Bernien et al. (2017), spatial correlations Schauß et al. (2012); Schwarzkopf et al. (2011); Schauß et al. (2015), strong optical nonlinearities Pritchard et al. (2010a); Dudin and Kuzmich (2012); Peyronel et al. (2012); Maxwell et al. (2013); Tresp et al. (2015); Firstenberg et al. (2016); Murray and Pohl (2017), plasma formation Robert-de Saint-Vincent et al. (2013), and photon-photon gate Tiarks et al. (2019). The single-photon nonlinearity arising from the strong interaction between Rydberg atoms shows great potential in constructing single-photon transistors Tiarks et al. (2014); Gorniaczyk et al. (2014); Baur et al. (2014). The fundamental aspects of quantum nonlinearity based on Rydberg atoms have been studied before; a type of "photonic hourglass" single-photon device is constructed Firstenberg et al. (2013); Peyronel et al. (2012). Such "photonic hourglass" is a kind of medium exhibiting strong absorption of photon pairs while remaining transparent to single photons. However, all the relative experiments on switching were demonstrated with a weak coherent field, thus there are no reports on switching of a true single-photon. Operating on true single photons is more challenging than attenuated coherent pulses.

Here, we demonstrate an experiment of switching true single-photons from entangle photon pairs. The entangled photon pairs are prepared in one atomic cloud and propagate through another atomic cloud for switching operation. The switching operation is using a single-photon level gate field to turn on or turn off the acceptance of that true single-photon. We perpare a gate pulse with 1$\sim$2 photons per blockade sphere to switch one of the entangled photons based on Rydberg blockade effect. By controlling the large nonlinearity offered by the long-range interaction from the Rydberg atoms, we can turn on and turn off the Rydberg electromagnetically induced transparency (Rydberg-EIT) window corresponding to the switch on and switch off operationPritchard et al. (2010a); Petrosyan et al. (2011). The measured coincidence counts with and without a gate field show an obvious switching effect of the entangled photons. The fidelity of the entangled state is $85.3\%\pm 1.5\%$ and $80.4\%\pm 2.3\%$ in the absence and presence of a gate field, respectively, with a switch contrast larger than $50\%$. By increasing the principal quantum number $n$, the switching effect becomes stronger and the required photon number of the gate field decreases. Implementing a Rydberg-mediated switch device under non-classical fields could enable the implementation of quantum computation and information processing with the interaction between Rydberg atoms and entangled photons Saffman et al. (2010), such as building a Toffoli gate Cory et al. (1998) and quantum computation Gorshkov et al. (2011); Khazali et al. (2015); Wade et al. (2016); Sun and Chen (2018) with Rydberg ensembles, and switching a distributed quantum node.

2. Results

2.1. Experimental setup

The sample media are optically thick atomic ensembles of Rubidium 85 (${}^{85}Rb$) trapped in different magneto-optic traps (MOTs), labeled MOT 1 and MOT 2. Schematics of the energy levels, time sequence, and experimental setup are shown in figure 1 (a)–(c). A cigar-shaped ${}^{85}Rb$ atomic ensemble is first prepared in MOT 1 and then cooled down to about 100 $\mu$K via the optical molasses technique; the atomic cloud has dimensions of $10\times 2\times 2$ $\textrm{mm}^{3}$. We prepare non-classical photon pairs by spontaneous four-wave mixing (SFWM) in this atomic ensemble. The energy levels involved here correspond to the double-$\Lambda$ system, consisting of both the D1 and D2 lines of Rubidium 85. The two pump fields couple the atomic transition $5S_{1/2}(F=3)\rightarrow 5P_{1/2}(F^{\prime}=3)$ with a detuning of $-2\pi\times 110$ MHz and the atomic transition $5S_{1/2}(F=2)\rightarrow 5P_{3/2}(F^{\prime}=3)$ under resonance. The generated signal photons (labeled signal 1 and signal 2) are correlated in the time domain. The signal-2 photon passing through an acousto-optic modulator (AOM) is frequency shifted by $+2\pi\times 120$ MHz, after which it is exactly resonant with the atomic transition $5S_{1/2}(F=3)\rightarrow 5P_{3/2}(F^{\prime}=4)$. Then, the signal-2 photon propagates through the three-dimensional ${}^{85}Rb$ atomic cloud in MOT 2 for the demonstration of the switching process. Finally, we perform quantum state tomography for the photonic entanglement before two signals are detected by two single-photon detectors. The coils of MOT 2 are switched off during the switching measurement. The spherical atomic cloud of MOT 2 has a size of $500\leavevmode\nobreak\ \mu$m with a temperature $\sim$ 20 $\mu$K and an average density of 3.5\times 10^{11}\textrm{c\textrm{m}^{-3}}. The coupling field is resonant with the atomic transition $5P_{3/2}(F^{\prime}=4)\rightarrow\left|nD_{5/2}\right\rangle$, that is $\Delta_{c}=0$. Rabi frequency of coupling light is $\Omega_{c}=2\pi\times 11$ MHz to demonstrate EIT and blockade configuration for single-photons.

The signal-2 photon has a beam waist of 16 $\mu\textrm{m}$ in the center of MOT 2 which is obtained by using a short-focus lens. With a pulsed coupling beam (TA-SHG, Toptica), we demonstrate Rydberg-EIT in the ladder-type atomic configuration, consisting of a ground state $\left|g\right\rangle$, an excited state $\left|e\right\rangle$, and a highly-excited state $\left|nD\right\rangle$; here, $n=50$. The gate field has a beam waist of 18 $\mu\textrm{m}$ in the center of MOT 2 and couples the atomic transition $5S_{1/2}(F=3)\rightarrow 5P_{3/2}(F^{\prime}=4)$. The coupling field with a beam waist of 30 $\mu\textrm{m}$ covers both the gate and signal-2 beams. The smaller the beam waist, the stronger the blockade effect Peyronel et al. (2012). However the beam size is limited to the size of the transmission window of our MOT. Analyzing the van der Waals interactions between the Rydberg atoms with an effective coefficient $\overline{C}_{6}=2\pi\times 32$ $\textrm{GHz}\cdot\mu\mathrm{m}^{6}$ for the rubidium 50$D_{5/2}$ by considering weighted average of the interaction effects of all Zeeman sublevels, we can calculate an average blockade radius $\sim$3.78 $\mu\textrm{m}$ with $\overline{r}_{b}=|\frac{\overline{C}_{6}}{\sqrt{(2\Delta_{c})^{2}+\Omega_{c}^{2}}}|^{1/6}$ Balewski et al. (2014) Šibalić et al. (2017). Since the coupling Rabi frequency is larger than the bandwidth of the signal photon, we use the strong coupling configuration to calculate the blockade radius. Figure 1(d) describes the switching effect on a weak coherent pulse, the red and blue lines represent the Rydberg-EIT spectra with and without a coherent gate field.

2.2. Bandwidth matching

In order to switch single photons, we need to connect two physical systems. One is to generate entangled photon; the other is to operate on that photon. We match the frequency and the bandwidth between the signal-2 photon and the absorption window of the atomic ensemble in MOT 2. This can be realized by changing the frequency and Rabi frequency $\Omega_{p2}$ of the pump 2 field as explained above. The switching effect obviously decreases when the bandwidth of signal-2 photon increases. Due to the narrow transparency window in the spectrum of Rydberg-EIT, the optical response on two-photon resonance is strongly affected by the level shifts induced by Rydberg atoms interaction and the linewidths of the input lasers Levine et al. (2018). Compared with $S$ state, $D$ state has wider transparency window resulting from the larger dipole matrix element to $D$ state. Thus, we use Rydberg-$D$ state to get larger bandwidth and higher transmission rate of Rydberg-EIT window.

As a result, the mismatching between the signal-2 photon and the absorbtion bandwidth of the atomic ensemble in MOT 2 decreases the switch contrast. Because the high-frequency component of the signal-2 photon is unable to fall within the Rydberg-EIT window, the reabsorption of the signal-2 photon weakens although the gate field is present. The switch contrast decreases with increasing Rabi frequency $\Omega_{p2}$ of pump 2 field (see figure 2). The bandwidth of the signal-2 photon depends significantly on $\Omega_{p2}$ Du et al. (2008); Liao et al. (2014), because the profile of the wave packet of the signal-2 photon can be modulated by tuning the $\Lambda$-EIT transparency window. The single-photon bandwidth becomes narrower with the $\Omega_{p2}$ decreasing. Only when the bandwidth of the single photon is narrower than the Rydberg-EIT window, can we get a higher absorption rate and switch contrast.This data in figure 2 hints that the switching effect becomes more obvious with a smaller $\Omega_{p2}$. For the optimized case $\Omega_{p2}\sim 2\pi\times 1$ MHz, the bandwidth of the signal-2 photon is at $\sim 2\pi\times 5$ MHz, and the absorption window for the atomic ensemble in MOT 2 is $\sim 2\pi\times 13$ MHz. That is, the signal-2 photon can completely fall within the Rydberg-EIT window. If decreasing $\Omega_{p2}$ further, the signal to noise ratio of two-photon coincidence becomes worse.

2.3. Switch entangled photons

To demonstrate the switching effect under quantum regime, we firstly prepared non-classical photon pairs via SFWM process Du et al. (2008); Liao et al. (2014) in MOT 1. The generated photon pairs are correlated in time domain. We construct two optical paths $L$ and $R$ by using two beam displacers (BDs) to build a passive-locking interferometer Ding et al. (2016); Zhang et al. (2016); Yu et al. (2018) where the perturbations between $L$ and $R$ optical paths can be mutually eliminated. The signal photons in each path are collinear, as the phase matching condition $k_{\mathrm{p1}}-k_{\mathrm{s1}}=k_{\mathrm{p2}}-k_{\mathrm{s2}}$ should be satisfied in the SFWM process. With two half-wave plates inserted in the $R$ optical path, the signal photons along these two optical paths can be coherently combined by BDs. The form of the entanglement is

[TABLE]

with $\theta$, the relative phase between $L$ and $R$ optical paths, setting to zero in our experiment; $\left|H_{s1,s2}\right\rangle$ and $\left|V_{s1,s2}\right\rangle$ represent the horizontal and vertical polarized states of the signal photons. The details about generating entangled photon pair are in our supplementary materials.

In order to demonstrate the switching effect of entangled photons, we input entangled photons into MOT 2. In this situation, we use a 50-m fibre to introduce a time delay in the path of the signal-1 photons. This guarantees that the entanglement does not collapse before the switching process has finished. The results are shown in figure 3(a) and (b); the former shows the coincidence counts of photon pairs when the atoms in MOT 2 are absent (red) and present (blue), whereas the latter shows the results under Rydberg-EIT without (red) and with (blue) gate field. Obviously, the coincidence counts decrease when the gate field is applied as the signal-2 photon is significantly absorbed when compared with the no-gate situation. The central physics behind the operation of a single-photon switch is that the long-range interaction between Rydberg atoms endows the Rydberg-EIT medium with a large optical nonlinearity Pritchard et al. (2010b); Peyronel et al. (2012), and the resulting dipole blockade effect makes the medium non-transparent. We define a switch contrast to characterize the switching effect,

[TABLE]

where $\mathrm{CC_{EIT}}$ and $\mathrm{CC_{gate}}$ represent the total coincidence counts between the signal-1 and signal-2 photons without and with a gate field. From the data [figure 3 (a) and (b)], we obtain a switch contrast of $\mathrm{C_{switch}}=77.6\%\pm 3.1\%$. The little peak in the rising edge comes from the high-frequency components of the single photons, which falls out of the absorption window of the atoms, [marked in blue color in figure 3 (a)]. In our experiment, the absorption window of atoms in MOT 2 is about $\sim 2\pi\times 13$ MHz. Although the bandwidth of the signal-2 photon wave-packet may be tuned by decreasing the power of pump 2 field Liao et al. (2014), there is always a high-frequency component in the wave-packet of the signal-2 photon. And the component falls outside of the bandwidth of the absorption, which induces an optical precursor Zhang et al. (2011); Ding et al. (2015). The switch contrast is also limited by the broadening effect of the Rydberg-EIT window, which is maybe caused by the dephasing of the distribution of Rabi frequencies with the unpolarized atoms in MOT 2. Our experiment is demonstrated with no bias magnetic fields. The atoms can be treated as averagely distributed in all sublevels.

We change the detected state $\varphi_{\mathrm{s2}}$ of the signal-2 photon and recorded the coincidence counts under different signal-1 states $\varphi_{\mathrm{s1}}$ of $\left|H\right\rangle$, $\left|V\right\rangle$, $\left|H\right\rangle-i\left|V\right\rangle$, and $\left|H\right\rangle+\left|V\right\rangle$. To obtain the differences with and without the gate field, we recorded these coincidence counts under these situations [figure 4 (a)–(d)]. The coincidence counts without (semi-transparent blue)/with (blue) the gate field are obviously different. We obtain switch contrasts with $\mathrm{C}_{\mathrm{switch}}^{VH}=81.0\%$, $C_{\mathrm{switch}}^{HV}=64.3\%$, $C_{\mathrm{switch}}^{RR}=52.2\%$, and $C_{\mathrm{switch}}^{DD}=79.9\%$ under the four situations $\varphi_{\mathrm{s1}}=\left|V\right\rangle$, $\varphi_{\mathrm{s2}}=\left|H\right\rangle$; $\varphi_{\mathrm{s1}}=\left|V\right\rangle$, $\varphi_{\mathrm{s2}}=\left|H\right\rangle$; $\varphi_{\mathrm{s1}}=\varphi_{\mathrm{s2}}=\left|H\right\rangle-i\left|V\right\rangle$ and $\varphi_{\mathrm{s1}}=\varphi_{\mathrm{s2}}=\left|H\right\rangle+\left|V\right\rangle$. The switching operation is effective for any polarization state with treating the signal-2 photon as if it were in a mixed state. The obtained switching contrasts are different depending on the detected states due to the non-perfect balance of the photon generation rate in the two optical paths and the noise of each path. In addition, we measure two-photon interference without and with the gate field under the signal-2 basis of $\left|H\right\rangle$ and $\left|H\right\rangle+\left|V\right\rangle$ [figure 4 (e) and (f)]. From figure 4 (e), we find the visibility without the gate field exceeding the threshold 70.7%, which means that the entanglement can be preserved after the transmission through the EIT window. It is easy to observe that the propagation of the signal-2 photon through the Rydberg-EIT medium doesn’t destroy the entanglement, because the Rydberg-EIT is independent on the polarization of the signal-2 photon.

We also perform quantum state tomography James et al. for the photonic entanglement to compare the entanglement properties before and after the switching process. Signal-1 and signal-2 are polarization entangled, their entangled state being $\left|\psi\right\rangle{\rm=}\left(\left|H\right\rangle_{\mathrm{s1}}\left|V\right\rangle_{\mathrm{s2}}+\left|V\right\rangle_{\mathrm{s1}}\left|H\right\rangle_{\mathrm{s2}}\right)/\sqrt{2}$. Using the polarizing beam splitter, half-wave plate, and quarter-wave plate, we project the two photon states onto the four polarization states $\left|\phi_{1\sim 4}\right\rangle$ ($\left|H\right\rangle$, $\left|V\right\rangle$, $\left(\left|H\right\rangle-i\left|V\right\rangle\right)/\sqrt{2}$, $\left(\left|H\right\rangle+\left|V\right\rangle\right)/\sqrt{2}$). We obtain a set of 16 data points from which to reconstruct the density matrix. By comparing with the ideal density matrix $\rho_{\mathrm{ideal}}$ using the formula $F_{i}{\rm{=Tr(}}\sqrt{\sqrt{\rho}{\rho_{{\rm{ideal}}}}\sqrt{\rho}}{{\rm{)}}^{2}}$, we obtain the fidelity to be $87.1\%\pm 2.5\%$ corresponding to the fidelity of input photons. By comparing with the input density matrix using the formula of $F{\rm{=Tr(}}\sqrt{\sqrt{\rho_{\mathrm{output}}}{\rho_{{\rm{input}}}}\sqrt{\rho_{\mathrm{output}}}}{{\rm{)}}^{2}}$, the fidelity for the output state without gate field is $85.3\%\pm 1.5\%$, and the state with gate field is $80.4\%\pm 2.3\%$. The switch contrast does not dramatically decrease before and after switch process. We use the initial fidelity for the input state to characterize the entanglement of the entangled photon pairs from SFWM process. Then, we want to demonstrate that our switching operation is a quantum process without any destructive effect to the input entanglement by calculating the fidelity for the output state with and without the gate field, respectively. We can still get high fidelity of the entanglement via much longer detecting time after the transmission through the EIT window, as if we hadn’t operated on it.

The nonlinearity of the medium not only depends on the atomic density, which determines the interaction distance, but also is strongly affected by the dipole interaction strength. We change the principal quantum number $n$ to change the interaction strength to measure both the Rydberg-EIT transmission contrast and the switch contrast. Here the Rydberg-EIT contrast is defined as $\mathrm{C_{EIT}=(CC_{no_{-}atom}-CC_{EIT})}\mathrm{/CC_{no_{-}atom}}$, $\mathrm{CC_{no_{-}atom}}$ representing the total coincidence counts between the signal-1 and signal-2 photons without atoms. We change the principal quantum number $n$ by changing the wavelength of the coupling laser. Each time we change the wavelength, we adjust the experimental optical system to keep the coupling Rabi frequency a constant. The results (figure 5) show that the Rydberg-EIT contrast decreases with the increase of $n$; this is because the transition amplitude for $\left|e\right\rangle\rightarrow\left|nD\right\rangle$ decreases. In contrast, because the dipole interaction strength increases, the switch contrast of the signal-2 photon obviously increases by comparing two situations, $n=60$ ($\overline{r}_{b}=5.12$ $\mu\textrm{m}$) and $n=40$ ($\overline{r}_{b}=1.05$ $\mu\textrm{m}$). The switch contrast is larger than 50% when $n>45$, revealing an effective switching operation. In this way, the interaction between Rydberg atoms becomes stronger with the principal quantum number increasing. Although the gate field has hundreds of photons because of the relatively large size of the atomic cloud in our experiment, we calculate that there are on average $1\sim 2$ gate photons per effective blockade sphere corresponding to the average energy of the gate field inside a blockade sphere expressed in units of $\hbar*\omega$. Eventually, the single-photon switch with a single gate photon can be realized by trapping the atoms into the scale of the blockade radius and increasing the principal quantum number $n$ .

3. Discussion

In addition, in order to avoid saturation of our switch system where the gate and coupling field would deplete the atoms after a certain duration, we set the experimental time window to 25 $\mu$s. The lifetime of Rydberg-excited atom is estimated to be $\sim$ 800 ns by measuring the Rydberg spinwave through storage process Ding et al. (2016); Wang et al. (2017), which guarantees an adequate interaction time for each switch operation during near 200 ns arrival time of the signal-2 photon given in figure 3. In our experiment, the dephasing of Rydberg $D$ state Tresp et al. (2015) is not obvious due to the small gate photon numbers used here. With small photon numbers as input, we have not investigated an obvious time dependence of the transmission on Rydberg-EIT resonance, but with an obvious time dependence of the transmission for large photon numbers, more details are shown in supplementary materials figure 2. Thus, the nonlinearity behind the switch experiment is offered by Rydberg blockade effect (see more details in supplementary materials figure 3). Besides, there are some challenges to improve the switch contrast: 1. Decreasing the bandwidth mismatch between signal-photon and the Rydberg-EIT transparency window. 2. Increasing the principle quantum number $n$ to achieve large dipole-dipole interaction strength, as shown in figure 5. 3. Trapping the atoms into the scale of the blockade radius. 4. Using a single-photon with ultra-narrow bandwidth. The bandwidth of transparency window of Rydberg-EIT with large principle quantum number $n$ would become narrower due to smaller natural line width for high-$n$ Rydberg state. This means that it needs narrower bandwidth of single-photon, such as subnatural-linewidth single-photon source Liao et al. (2014).

In summary, we have demonstrated an optical switch on entangled photons based on Rydberg nonlinearity with two atomic ensembles. The emitted signal-2 photon correlated with the signal-1 photon is blocked by another gate field under the Rydberg-EIT configuration. Switching effect depends on the principal quantum number, the bandwidth of the emitted single photons, and the average photon number of the gate field. We have successfully realized optical switch on one of the entangled photons of the pair, with more than 50% of pairs being blocked. These results on switching single photons using the strong dipole interaction hold promises in demonstrating quantum information processing between Rydberg atoms and entangled photons.

4. Acknowledgements

The authors thank Prof. Lin Li from huazhong university of science and technology and Prof. Yuan Sun from national university of defense technology for valued discussions and critical reading our manuscript. This work was supported by National Key Research and Development Program of China (2017YFA0304800), the National Natural Science Foundation of China (Grant Nos. 61525504, 61722510, 61435011, 11174271, 61275115, 11604322), Anhui Initiative in Quantum Information Technologies (AHY020200), and the Youth Innovation Pro motion Association of Chinese Academy of Sciences under Grant No. 2018490.