Efficient quantum memory for photonic polarization qubits generated by cavity-enhanced spontaneous parametric downconversion.

Interfaced single-photon sources and quantum memories for photons together form a foundational component of quantum technology. Achieving compatibility between heterogeneous, state-of-the-art devices is a long-standing challenge. We built and successfully interfaced a heralded single-photon source based on cavity-enhanced spontaneous parametric down-conversion in ppKTP and a matched memory based on electromagnetically induced transparency in warm $^{87}$Rb vapor. The bandwidth of the photons emitted by the source is 370 MHz, placing its speed in the technologically relevant regime while remaining well within the acceptance bandwidth of the memory. Simultaneously, the experimental complexity is kept low, with all components operating at or above room temperature. Read-out noise of the memory is considerably reduced by exploiting polarization selection rules in the hyperfine structure of spin-polarized atoms. For the first time, we demonstrate single-photon storage and retrieval in a ground-state vapor cell memory, with $g_{c,\text{ret}}^{(2)}=0.177(23)$ demonstrating the single-photon character of the retrieved light. Our platform of single-photon source and atomic memory is attractive for future experiments on room-temperature quantum networks operating at high bandwidth.

In quantum information science, photons are the best candidate for transmitting information, and atoms are the best candidate for storing information. The combination of these two systems provides a fascinating future for practical applications of the quantum information concepts. The work presented in this thesis mainly consists of two parts. The first part is about manipulation of entangled photons, including the demonstration of a nondestructive CNOT gate, the creation of narrowband entangled photons through cavity-enhanced spontaneous parametric down-conversion, and the realization of interference between narrowband photon sources. The second part is about manipulation of atomic ensembles. The main purpose for this part is to extend the quantum communication distance using the concept of quantum repeater. Within this part, the experimental work includes, the extension of storage lifetime of quantum memories to 1 ms by increasing the wavelength of stored spinwave, the realization of entanglement assisted spinwave interferometer, the demonstration of efficient entanglement swapping with quantum memories, and the realization of quantum teleportation between atomic ensembles.

Entangling quantum systems with different characteristics through the\nexchange of photons is a prerequisite for building future quantum networks.\nProving the presence of entanglement between quantum memories for light working\nat different wavelengths furthers this goal. Here, we report on a series of\nexperiments with a thulium-doped crystal, serving as a quantum memory for 794\nnm photons, an erbium-doped fibre, serving as a quantum memory for\ntelecommunication-wavelength photons at 1535 nm, and a source of photon pairs\ncreated via spontaneous parametric down-conversion. Characterizing the photons\nafter re-emission from the two memories, we find non-classical correlations\nwith a cross-correlation coefficient of $g^{(2)}_{12} = 53\\pm8$; entanglement\npreserving storage with input-output fidelity of\n$\\mathcal{F}_{IO}\\approx93\\pm2\\%$; and non-locality featuring a violation of\nthe Clauser-Horne-Shimony-Holt Bell-inequality with $S= 2.6\\pm0.2$. Our\nproof-of-principle experiment shows that entanglement persists while\npropagating through different solid-state quantum memories operating at\ndifferent wavelengths.\n

Precisely timed detection of single photons plays an important role in the field of quantum information processing and fluorescence sensing. The method of time-correlated single photon counting is therefore constantly evolving and the associated instrumentation is being improved with new ideas and technologies. Simultaneous, time tagged readout of multiple detector channels is invaluable in many applications, spanning from fluorescence lifetime imaging in biology to the measurement of quantum optical correlations in basic research. Here we present a new integrated design, providing up to three independent input channels, a very short dead time, very high throughput, and a timing resolution of 25 ps at reasonable cost and small size. Apart from design features and test results of the instrument, we show an application in quantum optics, namely, the measurement of the photon statistics of a heralded single photon source based on cavity-enhanced spontaneous parametric down-conversion.

In atomic-scale or quantum physics, an electromagnetic field is composed of photons, optical packets so small that a typical laser pointer with 1mW of power emits billions of them each second. Being able to take away or add a single photon in a light field at will would be useful for accurate engineering of quantum states. Such pure single photons are ideal for carrying and manipulating information in emerging quantum technologies, but generating them still is very challenging. In quantum physics, subtraction or addition of a photon is not a deterministic process. Instead, the probability is proportional to the number of photons originally in the electromagnetic field. This is described by the equation â|n〉 = √ n|n − 1〉 and â†|n〉 = √ n+ 1|n + 1〉, where â and ↠are annihilation and creation operators, respectively, representing the action of subtracting and adding a photon in a field composed of n photons.1 Such single-photon operations were limited to pure theoretical discussions until 2004, when Grangier and coworkers found a simple way to subtract a photon2 from a field. Passing through a beam splitter of high transmittivity, some photons can be split from the initial field. A ‘click’ detected in the photodetector in the reflected channel means one photon has been subtracted from the field: see Figure 1(a). When the initial field is composed of a small number of photons, the effect is dramatic and may even completely change the characteristics of the field. For example, let us take an initial single-mode squeezed state generated by ‘degenerate’ parametric down-conversion, which is an optical nonlinear process that converts a pump photon into two twin photons with half the pump photon energy. (This state is well known for its quantum noise squeezed into one quadrature at the expense of expanded noise in the other quadrature.) In order to visualize the noise properties and characteristics of the squeezed state, a probability-like function, such Figure 1. Setups to subtract (a) and add (b) a single photon from/to a light field. ρin and ρout denote the density operators of the input and output fields; BS is a low-reflectivity beam splitter; PDC is a nonlinear crystal where parametric down-conversion takes place; â and ↠denote on/off photodetectors.

We describe the simplest single–photon encoding schemes and introduce the concept of a quantum optical gate. These gates can be used to build up arbitrary entangled states of many initially separate single photons. Experimental realization of such a gate involves the development of nonlinear phase shift elements sensitice at the single quantum level. We report our experimental efforts using linear optical elements and non–classical sources where we are able to demonstrate interference and entanglement of initially separate single–photon pulses.

Electromagnetically induced transparency (EIT) is a well-known phenomenon due in part to its applicability to quantum devices such as quantum memories and quantum gates. EIT is commonly modeled with a three-level lambda system; however, this simplified model does not capture all the physics of EIT experiments with real systems. We present a theoretical study of the effect of two closely-spaced excited states on EIT and off-resonance Raman transitions. In addition to the expected broadening of the EIT resonance and reduction in EIT transparency due to multiple excited states, we find some unexpected and interesting results. A comparison with a model that does not allow for coupling of the excited states shows that the coherent interaction of the fields with two excited states whose separation is smaller than their Doppler broadened linewidth can enhance the EIT transparency under some conditions and can enhance and shift the resonance frequency of off-resonance Raman absorption. Furthermore, through a dressed state analysis of the full four-level system, we find that the underlying mechanism for the reduction in EIT transparency is a shift in the two-photon resonance due to unequal dipole moments of the transitions coupled by the control field. Complete transparency can only be recovered for systems with equal dipole moments or when the separation between the two excited states is at least of the order of the Doppler width. To support our theoretical study, we present experimental EIT measurements in the D1 lines of 85Rb and 87Rb that agree with our predictions of an enhancement or reduction of EIT transparency under specific conditions. The experimental results also verify the roles that the dipole moments and the separation between the two excited states have on recovering the EIT transparency.

We report an experimental realization of a narrow band polarization-entangled photon source with a linewidth of 9.6 MHz through cavity-enhanced spontaneous parametric down-conversion. This linewidth is comparable to the typical linewidth of atomic ensemble-based quantum memories. Single-mode output is realized by setting a reasonable cavity length difference between different polarizations, using of temperature controlled etalons and actively stabilizing the cavity. The entangled property is characterized with quantum state tomography, giving a fidelity of 94% between our state and a maximally entangled state. The coherence length is directly measured to be 32 m through two-photon interference.

We report an experimental demonstration of storage of photonic polarization qubit (PPQ) protected by dynamical decoupling (DD). PPQ's states are stored as a superposition of two spin waves by electromagnetically-induced-transparency (EIT). Carr-Purcell-Meiboom-Gill (CPMG) DD sequences are applied to the spin-wave superposition to suppress its decoherence. Thus, the quantum process fidelity remains better than 0.8 for up to 800 μs storage time, which is 3.4-times longer than the corresponding storage time of ~180 μs without the CPMG sequences. This work is a key step towards the storage of single-photon polarization qubit protected by the CPMG sequences.

Heralded single photons emitted from spontaneous four-wave mixing process in a cold atomic cloud have extremely long coherence time up to microseconds, due to slow light effect of electromagnetically induced transparency (EIT). The temporal state of these single photons is typically characterized by the photon counting approach. For the first time, we utilize balanced homodyne tomography (BHT) to fully characterize the temporal state. From reconstructing its density matrix, and further verify that the temporal state shaped through EIT window is pure. To further improve the mode matching between the optical field of Anti-Stokes and the local field in BHT, the driving beam of EIT is split from the local field, and frequency shifted using an electric-optic modulator. The characterization of the pure temporal-spectral state of the single photons paves the way for exploiting the temporal-spectral degree of freedom to develop photonic-quantum information processing.

Quantum networks are composed of quantum nodes which coherently interact by way of quantum channels. They offer powerful capabilities for quantum computation, communication, and metrology. A generic requirement for these realizations is the capability to generate and store quantum states among multiple quantum nodes, and to disseminate these resources throughout the network via the quantum channels. In this thesis, I describe a series of experiments whereby single excitations in atomic ensembles are strongly coupled to optical modes and provide efficient means for the coherent control of entangled states between matter and light. By following the seminal proposal by Duan et al., we have generated measurement-induced entanglement of an excitation between two cold atomic ensembles. Using this system, we investigated the relationship for the global bipartite entanglement and local correlations in its subsystems. In addition, we achieved functional quantum nodes for entanglement distribution. Two pairs of remote ensembles at two quantum nodes were prepared into entangled states in a heralded and asynchronous fashion by the conditional controls of the entanglement. The quantum states of the ensembles were then distributed into polarization entangled states of photons. We also prepared an analogous quantum state and transferred the nonlocal coherence between two pairs of heralded entangled atomic ensembles, providing a step towards entanglement connection. Beyond such probabilistic approaches, we demonstrated an experiment where entanglement between two quantum memories is created by the reversible and deterministic mapping of an entangled state of light via dynamic electromagnetically induced transparency. This experiment opens novel prospects of integrating hybrid quantum systems by way of reversible quantum interfaces between light and matter. Then, we extended our work to multipartite quantum systems. We theoretically investigated the characterization of multipartite mode-entangled states by way of quantum uncertainty relations, and introduced theoretical tools to verify the entanglement orders in multipartite systems. In particular, we achieved entanglement for one delocalized photon among multiple optical modes (N > 2). Finally, we have achieved measurement-induced entanglement of spin waves among four quantum memories. The individual atomic components for the entangled W state of the four ensembles were then coherently converted into four propagating entangled beams of light via superradiant emissions. We observed the statistical and dynamic transitions for the multipartite entangled spin waves. Experiments described in this thesis thereby represent significant advances of experimental and theoretical capabilities to generate, store, transfer, and characterize entanglement of matter and light over quantum networks.

This thesis is a summary of my research work during the last few years of my Ph.D. The main system of research is quantum memory based on cold atomic ensembles. Flying photons can be used to transmit quantum information over long distances, and quantum memories based on cold atomic ensembles can act as carriers for local storage and manipulation of quantum information, so it is of great significance to study cold atomic quantum memories for construction of global quantum networks. In this thesis, based on previous work, we further scrutinize the factors that will affect the performance metrics of quantum memory such as retrieval efficiency, and then we combine these analysis with some innovative experimental techniques, which will enable us to finally realize a highly retrievable quantum memory with intrinsic retrieval efficiency up to 90% and overall measured retrieval efficiency up to 40%. Based on this efficient quantum memory, we optimize the experimental loading time for preparing cold atomic ensembles, the number of experimental trials in each loading and other timing parameters, so that the experimental detection brightness of photons can support our experimental study of multiple quantum memories.

Storage and retrieval of parametric down-conversion (PDC) photons are demonstrated with electromagnetically induced transparency (EIT). Extreme frequency filtering is performed for the THz order of broadband PDC light and the frequency bandwidth of the light is reduced to the MHz order. Storage and retrieval procedures are carried out for frequency-filtered PDC photons. Since the filtered bandwidth (full width at half-maximum (FWHM)=9 MHz) is within the EIT window (FWHM=12.6 MHz), the flux of the PDC light is successfully stored and retrieved. The nonclassicality of the retrieved light is confirmed by using the photon counting method, where the classical inequality that is only satisfied for classical light fields is introduced. Since PDC photons can be utilized for producing a single-photon state conditionally, storage and retrieval procedures are also performed for conditional single photons. The anticorrelation parameter used for checking the property of the single-photon state shows a value of less than 1, which means that the retrieved light is in a nonclassical region.

Entangled photons are a crucial resource for linear optical quantum communication and quantum computation. Besides the remarkable progress of photon state engineering using atomic memories (Kimble (2008); Yuan et al. (2008)) the majority of current experiments is based on the production of photon pairs in the process of spontaneous parametric down-conversion (SPDC), where the entangled photon pair is concluded from post-selection of randomly occurring coincidences. Here we present new insights into the heralded generation of photon states (Barz et al. (2010); Wagenknecht et al. (2010)) that are maximally entangled in polarization (Schrodinger (1935)) with linear optics and standard photon detection from SPDC (Kwiat et al. (1995)). We utilize the down-conversion state corresponding to the generation of three pairs of photons, where the coincident detection of four auxiliary photons unambiguously heralds the successful preparation of the entangled state (Śliwa & Banaszek (2003)). This controlled generation of entangled photon states is a significant step towards the applicability of a linear optics quantum network (Nielsen & Chuang (2000)), in particular for entanglement distribution (Bennett et al. (1996)), entanglement swapping (Kaltenbaek et al. (2009); Pan et al. (1998)), quantum teleportation (Bouwmeester et al. (1997)), quantum cryptography (Bennett & Brassard (1984); Ekert (1991); Jennewein et al. (2000)) and scalable approaches towards photonics-based quantum computing schemes (Browne & Rudolph (2004); Gottesman & Chuang (1999); Knill et al. (2001)).

Using cavity-enhanced non-degenerate parametric down-conversion, we have built a frequency tunable source of heralded single photons with a narrow bandwidth of 8 MHz, making it compatible with atomic quantum memories. The photon state is 70% pure single photon as characterized by a tomographic measurement and reconstruction of the quantum state, revealing a clearly negative Wigner function. Furthermore, it has a spectral brightness of ~1,500 photons/s per MHz bandwidth, making it one of the brightest single photon sources available. We also investigate the correlation function of the down-converted fields using a combination of two very distinct detection methods; photon counting and homodyne measurement.