A scheme to utilize atomlike emitters coupled to nanophotonic waveguides is proposed for the generation of many-body entangled states and for the reversible mapping of these states of matter to photonic states of an optical pulse in the waveguide. Our protocol makes use of decoherence-free subspaces (DFSs) for the atomic emitters with coherent evolution within the DFSs enforced by strong dissipative coupling to the waveguide. By switching from subradiant to superradiant states, entangled atomic states are mapped to photonic states with high fidelity. An implementation using ultracold atoms coupled to a photonic crystal waveguide is discussed. DOI: 10.1103/PhysRevLett.115.163603 PACS numbers: 42.50.-p, 03.67.Bg, 42.50.Ex Recent work on optical emitters coupled to onedimensional (1D) waveguides has opened new avenues to investigate light-matter interactions [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. Particularly promising are the setups where atoms are strongly coupled to structured dielectrics [6][7][8][9][10], where large Purcell factors have been predicted [21,22]. Furthermore, collective effects can be enhanced by placing the atoms at particular positions [15,16,[23][24][25][26][27][28][29]. The combination of atomlike emitters and nanophotonic waveguides may enable new regimes for the interaction of light and matter, leading to technologies that outperform current ones and qualitatively different physics. In this work we investigate the possibility of using atom nanophotonics interfaces to tailor arbitrary states for propagating photons on demand, which lies at the heart of many quantum information [30], metrology [31], and lithography [32] methods (see Ref.[33] for a review). We predict large fidelities even for relatively large numbers of photons, something which has been impossible to achieve with other platforms in the optical domain.Our proposal uses N þ 1 three-level systems (with levels fjgi; jsi; jeig), where one of the optical transitions (jgi ↔ jei) is strongly coupled to a 1D waveguide [see Figs. 1(a) and 1(b)]. We denote by P 1D the Purcell factor corresponding to that transition, i.e., the ratio of the emission rate into the waveguide mode, Γ 1D , and the one for all other modes, Γ Ã . The atoms must be separated by distances proportional to λ a ¼ 2π=qðω a Þ, where qðωÞ is the wave number determined by the waveguide dispersion relation. Depending on their internal state, atoms may experience a collective decay into the waveguide, or become completely decoupled from it. The latter occurs if they are in a decoherence free subspace (DFS) [34][35][36]. Our protocol consists of two steps: in the first one, we generate certain states within the DFS, jΨ D i, by driving the atoms with lasers and using the collective quantum Zeno effect [37][38][39] within the DFS with an infidelitywhere m is the maximum number of photons we want to generate; in the second one, a laser pulse takes the atomic state out of the DFS so that atoms collectively emit into the waveguide, creating...

The interaction of quantum emitters with one-dimensional photon-like reservoirs induces strong and long-range dissipative couplings that give rise to the emergence of the so-called decoherence free subspaces (DFSs) which are decoupled from dissipation. When introducing weak perturbations on the emitters, e.g., driving, the strong collective dissipation enforces an effective coherent evolution within the DFS. In this work, we show explicitly how by introducing single-site resolved drivings, we can use the effective dynamics within the DFS to design a universal set of one and two-qubit gates within the DFS of an ensemble of two-level atom-like systems. Using Liouvillian perturbation theory we calculate the scaling with the relevant figures of merit of the systems, such as the Purcell factor and imperfect control of the drivings. Finally, we compare our results with previous proposals using atomic Λ systems in leaky cavities.

Engineering quantum states of light is at the basis of many quantum technologies such as quantum cryptography, teleportation, or metrology among others. Though, single photons can be generated in many scenarios, the efficient and reliable generation of complex single-mode multiphoton states is still a longstanding goal in the field, as current methods either suffer from low fidelities or small probabilities. Here we discuss several protocols which harness the strong and long-range atomic interactions induced by waveguide QED to efficiently load excitations in a collection of atoms, which can then be triggered to produce the desired multiphoton state. In order to boost the success probability and fidelity of each excitation process, atoms are used to both generate the excitations in the rest, as well as to herald the successful generation. Furthermore, to overcome the exponential scaling of the probability of success with the number of excitations, we design a protocol to merge excitations that are present in different internal atomic levels with a polynomial scaling. DOI: 10.1103/PhysRevLett.118.213601 On-demand generation of optical propagating photons is at the basis of many applications in quantum information science, including multipartite teleportation [1], quantum repeaters [2], cryptography [3,4], and metrology [5]. While single photons are routinely produced in different experimental setups [6], e.g., by using natural or artificial atoms coupled to cavities or waveguides [7][8][9][10][11][12], single-mode multiphoton states are much harder to generate [13]. Current methods are limited by either exponentially small success probabilities or low fidelities. The enhancement of light-matter interactions provided by quantum nanophotonics opens up new avenues to create high-fidelity multiphoton states. For example, m quantum emitters can be strongly coupled to structured waveguides, which show large Purcell factors, P 1D , so that m atomic excitations can be mapped to a waveguide mode with an error (or infidelity, I m ) scaling as m=P 1D . However, the resulting state is not a single mode, but a complex entangled state of several modes [14], so that it cannot be directly used for quantum information purposes. Single-mode multiphoton states can be created by storing m collective excitations in N ≫ m atoms, which are then mapped to a photonic state of the waveguide. While the latter process can be achieved with very low infidelity, scaling as m 2 =ðNP 1D Þ [14,15], present schemes for the first part scale like I m ∝ m= ffiffiffiffiffiffiffiffi P 1D p [14], as they still do not fully exploit the strong coupling to the waveguide nor collective effects. This ultimately limits the fidelity of the whole procedure.In this work we show how to overcome this limitation with new schemes for the heralded generation of m collective excitations in N ≫ m atoms coupled to a waveguide. The idea is to use the atoms to both create the excitations one by one, and to herald the success of the process. In this way, arbitrarily sma...

Photonic states with large and fixed photon numbers, such as Fock states, enable quantum-enhanced metrology but remain an experimentally elusive resource. A potentially simple, deterministic and scalable way to generate these states consists of fully exciting N quantum emitters equally coupled to a common photonic reservoir, which leads to a collective decay known as Dicke superradiance. The emitted N -photon state turns out to be a highly entangled multimode state, and to characterise its metrological properties in this work we: (i) develop theoretical tools to compute the Quantum Fisher Information of general multimode photonic states; (ii) use it to show that Dicke superradiant photons in 1D waveguides achieve Heisenberg scaling, which can be saturated by a parity measurement; (iii) and study the robustness of these states to experimental limitations in state-of-art atom-waveguide QED setups.Quantum metrology exploits quantum resources, such as squeezing and entanglement, to enhance the precision of measurements beyond the capabilities of any classical scheme [1][2][3][4]. Given N probes to estimate an unkown parameter ϕ, classical measurements are limited by the shot-noise limit (SNL) ∆ϕ = 1/ √ N , whereas entangled probes can surprass this bound possibly reaching the Heisenberg limit (HL), ∆ϕ = 1/N , which in fact provides the ultimate bound on sensitivity. In atomic ensembles, achieving quantum-enhanced metrology with relatively large particle numbers appears possible [5][6][7][8][9][10][11][12][13]. The situation becomes more challenging when dealing with photonic states in optical interferometry. Squeezed states, a well known-resource [14], are very challenging to scale up, with current demonstrations being at the few-photon level [15,16]. States with a well-defined photonic number, e.g. NOON [17] and twin-Fock [18] states, also constitute a powerful resource, which has been experimentally tested for few-photons states [19][20][21]. Yet, current experimental methods to generate these states are limited by both low fidelities and efficiencies, since they are based in combining heralded single-photons with post-selection, which naturally leads to an exponential decrease of the efficiency with increasing N [22, 23].A promising approach for generating multiphoton states in a deterministic, efficient and scalable manner are quantum emitters coupled to photonic waveguides [24][25][26][27][28][29][30][31][32]. In these setups, the waveguide decay rate, Γ 1d , can exceed the free space one, Γ * , and naturally enhance the photon collection efficiency of the system. On top of that, when all the quantum emitters couple equally to the waveguide, their dynamics is described by the celebrated Dicke model [33], which predicts an additional collective enhancement of the waveguide decay rate. Given N emitters in the waveguide and m collective atomic excitations, previous studies focused on the regime m N [34], where the m collective excitations decay into a single-mode m-photon wavepacket with an error scaling as ε lin ...

In multi-level systems, the commonly used adiabatic elimination is a method for approximating the dynamics of the system by eliminating irrelevant, non-resonantly coupled levels. This procedure is, however, somewhat ambiguous and it is not clear how to improve on it systematically. We use an integro-differential equation for the probability amplitudes of the levels of interest, which is equivalent to the original Schrödinger equation for all probability amplitudes. In conjunction with a Markov approximation, the integro-differential equation is then used to generate a hierarchy of approximations, in which the zeroth order is the adiabatic-elimination approximation. It works well with a proper choice of interaction picture; the procedure suggests criteria for optimizing this choice. The first-order approximation in the hierarchy provides significant improvements over standard adiabatic elimination, without much increase in complexity, and is furthermore not so sensitive to the choice of interaction picture. We illustrate these points with several examples. arXiv:1209.6568v2 [quant-ph]