Quantum memories for optical and microwave photons provide key functionalities in quantum processing and communications. Here we propose a protocol well adapted to solid state ensemble based memories coupled to cavities. It is called Stark Echo Modulation Memory (SEMM), and allows large storage bandwidths and low noise. This is achieved in a echo like sequence combined with phase shifts induced by small electric fields through the linear Stark effect. We investigated the protocol for rare earth nuclear spins and found a high suppression of unwanted collective emissions that is compatible with single photon level operation. Broadband storage together with high fidelity for the Stark retrieval process is also demonstrated. SEMM could be used to store optical or microwave photons in ions and/or spins. This includes NV centers in diamond and rare earth doped crystals, which are among the most promising solid-state quantum memories.PACS numbers: 03.67. Lx,76.30.Kg,76.60.Lz Quantum memories (QM) are essential components in quantum information processing. They enable storage and on-demand retrieval of quantum states and allow using fast but short-lived processing qubits, or photonic states that are excellent carriers of quantum information but are difficult to store. QM for light find applications in linear optics quantum computing, as well as in quantum communications and networks, where they could enable distribution of entangled states over long distances using quantum repeater architectures [1,2]. There is also a growing interest in spin based quantum memories that store micro-wave photons which in turn can be interfaced to superconducting qubits [3]. In the solid state, optical and microwave QM based on inhomogeneously broadened ensemble are actively investigated in rare earth (RE) ion doped crystals and diamonds containing NV centers [4-9] These two systems are well adapted to highly multimode storage, where multiple photons with large bandwidths are stored for long times [10]. Moreover, high efficiency can be obtained by coupling these centers to a cavity, overcoming their weak interactions with photons, either for spin or optical transitions [11][12][13]. A natural protocol to implement QM in inhomogeneous ensembles is the spin or photon echo [14,15] which recovers the initial excitation of the system by applying a π pulse to the storage transition. This inverts the atomic or spin phase evolution and results in a collective emission, the so-called echo. However, this scheme does not allow low-noise operation, a key parameter for quantum memories, which must store photonic qubits like single photons [16]. This is because the collective emission occurs in an inverted medium which produces a too large spontaneous emission at the memory output. To avoid this situation, several protocols have been proposed and experimentally investigated. However, they require spectral tailoring [17][18][19][20][21], which requires a long lived storage level and can reduce bandwidth, or particular spatial phase matching conditions...

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