Quantum metrology with one-dimensional superradiant photonic states

Abstract

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 ...

Multimode Fock states with large photon number: effective descriptions and applications in quantum metrology

“…We now apply the machinery developed in the previous section to the characterisation of superradiant photonic states emitted when N excited atoms are placed next to the waveguide in the atomic mirror configuration, as previously proposed by us in [20]. This corresponds to taking |φ (N ) in (11) with γ n = Γ 1d n(N − n + 1) and ω n = nω 0 .…”

“…Given this highly non-trivial state, the main contributions of this article are: tential for quantum metrology [1][2][3][4]. Building on our previous work [20], our goal is to extend well known results in quantum optical interferometry [39,40] to the presence of a nontrivial multimode structure within the input photonic states, as in Eq. (1).…”

“…An illustration of that is the proposal put forward by us in Ref. [20] to generate multiphoton states with quantum emitters coupled to photonic waveguides [21][22][23][24][25][26][27][28][29][30]. There, N excited emitters interact with the waveguide in the so-called mirror configuration [28,31], such that its dynamics is described by the well-known Dicke model [32].…”

Metrological Nonlinear Squeezing Parameter

“…Fock states |N = (â † ) N / √ N!|0 have particularly appealing properties for displacement amplitude sensing. They can be generated in a variety of quantum systems, e.g., by manipulating the motion of trapped ions [83], by strong atomcavity interactions [45], or by optical nonlinear [55] or superradiant processes [84]. Due to their isotropic concentric fringes in phase space, Fock states yield sub-shot-noise sensitivity for any displacement generated byq n .…”

Coherent amplification and inversion less lasing of surface plasmon polaritons in a negative index metamaterial with a resonant atomic medium

“…The robustness of amplification depend on low SPP field propagation and robust directional (17) www.nature.com/scientificreports/ SSPP launching. Due to loss-compensation scheme, we expect the stable propagation of SPP field and hence robust amplification of SPP field is produced only for robust SSPP, which is achieved as waveguide decay rate (Ŵ W ) exceed the free-space one (Ŵ F ) 83 . For our hybrid waveguide the decay rate is controllable, Ŵ W = 5 × 10 −3 γ F , and a specific case of m = N a is also achievable.…”