Realization of a cascaded quantum system: heralded absorption of a single photon qubit by a single-electron charged quantum dot

TL;DR

This paper demonstrates a heralded quantum state transfer between two quantum dots separated by 5 meters, using a measurement that confirms successful transfer without revealing qubit information, advancing quantum network capabilities.

Contribution

It introduces a method for heralded absorption of a photonic qubit by a distant quantum dot, enabling quantum information transfer without qubit information leakage.

Findings

Successful heralded absorption of a single-photon qubit by a distant quantum dot.

Quantum information transfer occurs without revealing the qubit state.

Potential for new quantum information protocols using cascaded quantum systems.

Abstract

Photonic losses pose a major limitation for implementation of quantum state transfer between nodes of a quantum network. A measurement that heralds successful transfer without revealing any information about the qubit may alleviate this limitation. Here, we demonstrate heralded absorption of a single photonic qubit generated by a single neutral quantum dot, by a single-electron charged quantum dot that is located 5 meters away. The transfer of quantum information to the spin degree of freedom takes place upon emission of a photon: for a properly chosen or prepared quantum dot, detection of this photon yields no information about the qubit. We show that this process can be combined with local operations optically performed on the destination node, by measuring classical correlations between the absorbed photon color and the final state of the electron spin. Our work suggests alternative avenues for realization of quantum information protocols based on cascaded quantum systems.

Figures

d). The time-resolved detection rate exhibits a beat note at $\omega_{blue}-\omega_{red}=4.9$ GHz, whose visibility is limited by the jitter of our detector. The $g^{(2)}(0)$ of the single-photon pulses is measured to be $0.15\pm 0.02$, limited by double excitations during the 400 ps laser pulse. When the crossed polarizer is set, the photons at frequency $\omega_{diag}$ scattered by QD2 can then be observed (blue curve in Fig. [2](#S0.F2)d). We also verify once more that the counts vanish when either dot is switched off-resonance (orange and purple curves on Fig. [2](#S0.F2)d).

d). The time-resolved detection rate exhibits a beat note at $\omega_{blue}-\omega_{red}=4.9$ GHz, whose visibility is limited by the jitter of our detector. The $g^{(2)}(0)$ of the single-photon pulses is measured to be $0.15\pm 0.02$, limited by double excitations during the 400 ps laser pulse. When the crossed polarizer is set, the photons at frequency $\omega_{diag}$ scattered by QD2 can then be observed (blue curve in Fig. [2](#S0.F2)d). We also verify once more that the counts vanish when either dot is switched off-resonance (orange and purple curves on Fig. [2](#S0.F2)d).

Full text

In the context of quantum communication and distributed quantum computing, the ability to faithfully transfer a quantum state from one node to another is of key importance DiVincenzo00 . In a direct transfer scheme, quantum information would in principle be transmitted between nodes using consecutive emission, propagation and absorption of single optical photons Cirac97 ; Rezus12 ; Meyer15 ; Piro10 . However realization of such a full procedure is most challenging in any physical system, due to inefficient photon collection from single-photon sources as well as propagation losses. Previous realization of such transfer using atoms was achieved with low efficiency and without an experimental verification of successful transfer Ritter12 . On the other hand, a heralding signal, provided for instance by detection of a subsequently emitted photon at a different wavelength, can make the transfer process robust to losses in protocols where multiple attempts are possible. Previous demonstrations of heralded photon-to-matter state transfer with atoms or NV centers were implemented using classical light pulses from weak lasers Kurz14 ; Kalb15 ; Yang16 instead of true single photon pulses generated by a single quantum system. A heralded transfer of quantum information from a single flying qubit to a single stationary qubit has so far remained elusive.

In this Letter, we demonstrate heralded absorption of a single photonic qubit by a single-electron charged quantum dot (QD). Our work constitutes an experimental realization of a cascaded quantum system Carmichael93 ; Gardiner93 , where fluorescence from a source quantum emitter (a neutral QD) is used to drive a second target quantum emitter (a single electron charged QD); the detection of a photon from the latter heralds the success of single photon absorption. Furthermore, we show that the color of the photon generated by the source QD is classically correlated with the spin state of the electron in the target QD upon completion of the transfer process. The scheme we realize requires that the source and the target QD have energy level diagrams depicted in Figure 1a: the neutral exciton fine structure allows for the possibility to generate a photonic color qubit in an arbitrary superposition of two center frequencies $\omega_{blue}$ and $\omega_{red}$ Gao13 . Degeneracy of the diagonal transitions of the target QD on the other hand, is essential for heralding the absorption of the incoming photonic qubit in state $\alpha|\omega_{red}\rangle+\beta|\omega_{blue}\rangle$, without revealing any information about the qubit state. Provided that the electron spin is initially prepared in a superposition state $\left(|\uparrow\rangle+|\downarrow\rangle\right)/\sqrt{2}$, the absorption of the incoming photon and the subsequent emission of a diagonal photon at frequency $\omega_{diag}$ projects the electron spin onto the state $\alpha|\uparrow\rangle+\beta|\downarrow\rangle$. By choosing a single-electron charged source QD, this scheme can be modified to obtain spin-to-spin quantum state transfer or heralded entanglement generation (see Supplemental Material SOM ).

Self-assembled QDs are one of the most favorable systems for building efficient quantum links between remote nodes using optical photons Gao13 ; Delteil15 , due to their integrability into microcavities that allow efficient photon collection into fibers Gazzano13 ; Munsch13 and near-unity quantum efficiency of emission into a zero-phonon-line. In this work, we use two identical samples of single self-assembled InGaAs/GaAs QDs embedded in a lossy planar cavity consisting of a bottom thick (28 periods) distributed Bragg mirror (DBR) and a top thin (2 periods) DBR. A p-i-n diode structure is grown around the QD layer for charge state control and Stark tuning of the transitions. A ZnO solid immersion lens (SIL) is mounted on top of the samples to increase the collection efficiency. The samples are held in two helium bath cryostats with confocal microscopes allowing to excite QDs with lasers and collect scattered photons through the same objective.

The experimental set-up is depicted Fig. 1b: single photon pulses are generated through resonant optical excitation of a neutral QD (labeled QD1). By making use of the exciton fine structure, single photons can be generated in any superposition of two center frequencies $\omega_{blue}$ and $\omega_{red}$ Gao13 . They are conveyed via a fiber to another QD located 5 meters away (QD2), which is charged with a single electron. An external magnetic field is applied to QD2 in Voigt geometry, making all four transitions from the two trion states to the two spin ground states allowed, with equal oscillator strength. Moreover, QD2 has been selected to have its two diagonal transitions almost degenerate, which is ensured by opposite in-plane $g$-factors for the electron and the hole. Although such QDs can be naturally found in self-assembled QD samples (see Supplemental Material SOM ), the diagonal transitions can also be tuned to resonance using external electric field Pretchel15 , strain Tholen16 , ac-Stark shift Bose12 or magnetic field orientation using a vector-magnet.

Fig. 1c shows resonance fluorescence (RF) plateaus of the two QDs. While QD1 RF exhibits standard fine-structure-split lines of the neutral exciton, QD2 RF exhibits unique signature of degenerate diagonal transitions: instead of four RF lines visible only near the edges of the plateau due to spin pumping Xu07 , only three lines are visible. Moreover, the intensity of the intermediate RF line does not vanish in the middle of the gate voltage range since a laser at $\omega_{diag}$ ensures that there is no spin pumping. The external electric and magnetic fields are adjusted such that the two transitions of QD1 match the blue and red vertical transitions of QD2, as indicated in Fig. 1c. For QD2, we have carried out Hong-Ou-Mandel interferometry to verify the indistinguishability of photons emitted at $\omega_{diag}$ (see Supplemental Material SOM ).

The first part of our demonstration consists in exciting QD1 with a two-color laser in cw, generated from a single-mode laser using an electro-optic modulator (EOM) driven with a microwave signal at $(\omega_{blue}-\omega_{red})/2$. The resonant fluorescence photons are brought to the second cryostat, and their polarization is made vertical ($V$). The photons that are scattered a second time by QD2 pass through a horizontally ($H$) oriented polarizer that suppresses reflected QD1 light, such that we collect only diagonal photons at frequency $\omega_{diag}$. The collection path also includes a grating of bandwidth $\sim 80$ GHz and a flip-mounted Fabry-Pérot filter (that we do not use in this part of the experiment). Finally, we placed a superconducting single-photon detector (SSPD) at the output port of the collection fiber. Its dark count rate is lower than 1 s*-1*, and so is the background light detection rate, leading to a false events recording rate lower than 2 s*-1*, which is essential for the experiments presented here.

When we fix the laser wavelength and the gate voltage of QD2 at resonance, the count rate shows a Lorentzian line shape as a function of QD1 gate voltage, with a maximum of about 90 counts per second (Fig 2a). Fixing QD1 and varying QD2 leads to a similar result (Fig 2b). When either dot is tuned off resonance, the count rate remains as low as 2 s*-1*, close to the background value, irrespectively of the gate voltage of the other dot (red curves of Fig 2a and Fig 2b), demonstrating unequivocally that we have implemented heralded single photon absorption. For these measurements, the laser power is set close to the saturation power of QD1, corresponding to the detection of about $5.5\cdot 10^{6}$ counts/s at the output fiber of the first cryostat (point $A$ on Fig. 1a). Although QD1 can be driven at higher power, leading to a detection rate up to almost 10 million counts/s, it does not result in an increase of the heralded absorption rate. Indeed when increasing the power above saturation, the photons emitted by QD1 start having a spectral mismatch with QD2 transitions, attributed to the appearance of Mollow sidebands Vamivakas09 ; Flagg09 . These sidebands can be directly observed by means of the heralded scattering rate as a function of the gate voltage of QD2 as can be seen on Fig. 2c.

The quantum efficiency of the heralded absorption process can be estimated knowing the total transmission of our set-up ($\sim$ 0.3 %, measured from $A$ to $B$ on Fig. 1a) and taking into account the collection efficiency of the scattered photons, including the collection at the first lens (20 %, deduced from the maximum count rate and the measured excited state lifetime) and the polarizer (blocking 50 % of the scattered photons). We deduce that about 8 % of the incident photons are absorbed by QD2. This experiment is done with random spin population of QD2, leading to an additional reduction of 50 % in this probability – the quantum efficiency is therefore estimated to be about 16 %. This number is consistently close to the overlap of QD2 emission with the free-space mode collected by the microscope objective ($\sim 20$ %) which gives the maximum absorption probability of a single incident photon by a single quantum emitter Pinotsi08 .

This experiment can also be performed in pulsed regime, allowing to observe the dynamics of the process within a few tens of picoseconds (Fig. 2d). In this case, QD1 is driven by a two-color laser pulse of 400 ps, generating two-color single photon pulses with a repetition rate of 152 MHz. They can be directly detected by removing the cross-polarization suppression (green curve of Fig. 2d). The time-resolved detection rate exhibits a beat note at $\omega_{blue}-\omega_{red}=4.9$ GHz, whose visibility is limited by the jitter of our detector. The $g^{(2)}(0)$ of the single-photon pulses is measured to be $0.15\pm 0.02$, limited by double excitations during the 400 ps laser pulse. When the crossed polarizer is set, the photons at frequency $\omega_{diag}$ scattered by QD2 can then be observed (blue curve in Fig. 2d). We also verify once more that the counts vanish when either dot is switched off-resonance (orange and purple curves on Fig. 2d).

The time-resolved detection of these doubly scattered photons well above the background opens the possibility to implement quantum information protocols based on such cascaded quantum systems, by combining heralded absorption of photonic qubits with local operations such as state initialization, manipulation and readout. In the following, we demonstrate an experimental implementation of a photon-to-spin state transfer protocol, and we show classical correlations between the photonic qubit state and the final spin state.

The set-up for this experiment is the same as depicted in Fig. 1a SOM . The pulse sequence is shown Fig. 3a. The spin state of QD2 is prepared in a superposition of equal weights by spin pumping in $|\uparrow\rangle$ or $|\downarrow\rangle$ followed by a rotation of $\pi/2$ performed using a 15-picosecond laser pulse detuned by 1 THz from the trion resonances. This rotation requires the insertion of a quarter-wave plate in the input arm such that the excitation port is elliptically polarized Press08 . As a consequence, the crossed-polarized detection path is also elliptically polarized and therefore does not reject all the $V$-polarized blue and red photons scattered by QD2. They are then filtered out by adding a Fabry-Pérot filter in the collection path, having one of the transmission maxima centered at $\omega_{diag}$. A single photon pulse, generated by the excitation of QD1 exciton, is coupled to QD2 after a delay time of $\sim 15$ ns, chosen such that the trion population has sufficiently decayed to observe heralded absorption above the spontaneous emission background. After an additional time of 25 ns (corresponding to the detector dead time), the pulse sequence is repeated, and the subsequent spin pumping pulse serves to measure the spin state in the computational basis states. As we do not perform dynamical decoupling, the spin superposition precesses with a random frequency during the protocol. Since in this work we demonstrate only classical correlations, this random phase plays no role in the obtained results. A detailed scheme of the experimental set-up including generation and synchronization of the optical pulses is available in the Supplemental Material SOM .

Fig 3b shows a time trace recorded during four hours. One of the major technical difficulties is to keep a low background – at least in the vicinity of the time window where we detect heralded absorption – when combining strong resonant laser pulses of $P\sim P_{sat}$ with the single photon pulses. As usual EOMs have finite on/off ratios (typically $10^{2}$ to $10^{3}$) leading to a constant RF background of a few thousands of counts per second (for a dot showing a few $10^{6}$ counts per second around saturation), we cascade three EOMs to reach on/off ratio of $10^{6}$. This in turn suppresses the scattered photon background and allows for observation of heralded absorption (see Supplemental Material SOM for more details about contributions to the background).

The four combinations of input photon color (red and blue) and spin state measurement ($|\uparrow\rangle$ and $|\downarrow\rangle$) are alternated, and classical correlations between the photon color and the spin state are deduced from the two-fold coincidences of a first photon detected during the heralded absorption window (green shading on Fig. 3b) together with a photon detected during the following spin pumping pulse (orange shading on Fig. 3b). Using a repetition rate of 20 MHz, we obtain a success rate (rate of heralded absorption events) of 0.75 s*-1*, corresponding to the count rate in the green shaded time window in Fig. 3b. It is smaller than the rate shown in Fig. 2d due to the much lower repetition rate, as well as the use of elliptic polarization in both input and output arms and the FP filter transmission. This leads to a two-fold coincidence rate of 2.6 per hour. The result from data recorded during 46 h is shown in Fig. 3c. For a red (blue) input photon, the spin is measured in $|\uparrow\rangle$ ($|\downarrow\rangle$) $\sim$ 3.5 times more often than in $|\downarrow\rangle$ ($|\uparrow\rangle$), consistent with what is expected (cf. QD2 level scheme on Fig. 1a). It leads to a computation basis fidelity of $0.76\pm 0.16$, mainly limited by the background photons during the heralded absorption process.

Our experiments implement a cascaded quantum system where a single photon in a superposition of two color-states generated by a quantum emitter drives another quantum emitter with a spin-$1/2$ ground-state Carmichael93 ; Gardiner93 . While heralding of the photon absorption allows us to measure classical correlations between the photonic input and the output spin states, the current success rate is not high enough to implement state transfer in a quantum network. If the success rate can be enhanced, then heralded quantum state transfer can be combined with quantum error correction. More specifically, lack of a heralding event could act as a syndrome measurement for an erasure code that could be used to increase the success rate of quantum state transfer. Moreover, extensions of this work can also apply to the realization of hybrid quantum networks connecting different physical systems via photons Meyer15 .

The Authors acknowledge many useful discussions with M. Kroner, W.B. Gao and E. Togan. This work is supported by NCCR Quantum Photonics (NCCR QP), the research instrument of the Swiss National Science Foundation (SNSF), and by the Swiss NSF under Grant No. 200020-159196.