Looking inside an optical cavity with trapped ions

Quantum theory tells us that light shows both wave and particle nature. The behavior of light is described as an electromagnetic wave as well as a discrete quantum, so called `photon. Starting from the 1950s, quantum physicists have imagined how to trap photons. One approach is to build a box made out of two parallel mirrors with high reflectivity. Once a photon is injected into the box, the photon stays in it while bouncing back and forth between two mirrors. This box is called a `cavity. In practice, the reflectivity cannot be unity therefore photons leave the cavity in a given lifetime. The cavity has played a central role in investigations of classical optics, quantum optics, and quantum information science. Since the 1990s, physicists have thought of a nondestructive detection scheme of photons inside a cavity. It is necessary to perform such measurements because nonclassical quantum states are very fragile against the loss of photons through the cavity mirrors. The character of nonclassicality is also very different between the internal cavity field and output field. In the last decades, researches along the direction has been intensively explored in the microwave domain. However, it is still impossible to measure the internal fields of an optical cavity due to lots of technical difficulties. Here, we propose two fundamental quantum optics experiments to measure quantum states of photons inside an optical cavity. The first project is to measure the photon-number distribution in an optical cavity. We employ trapped calcium ions in a cavity, which is a nondestructive probe for the cavity photons. We can position a calcium ion at the center of the cavity by using external electric field. This calcium ion experiences energy level shifts determined by the number of photons in the cavity. Precision spectroscopy will be used to resolve photon-number-dependent level shifts, to reveal the quantized nature of the electromagnetic field. The second project is to generate Fock states, that is, photon-number states in the cavity, using a several ions. The ions will play two roles: An ancilla ion will be used to measure the intracavity photon statistics with the aforementioned scheme. The other ions will be addressed with a well-controlled pump laser in order to manipulate the photon statistics, ultimately leading to the generation of tailored Fock states. The meaning of the present proposal is that it is the first nondestructive measurement of the internal quantum state of an optical cavity. The successful realization of the proposal will open up various possibilities in the area of quantum optics and quantum information science, including unit-efficiency photon detectors and nondestructive detection of Schrodinger cat states in the optical cavity domain.

In this Lise Meitner program titled Looking inside an optical cavity with trapped ions, we performed an experimental research on the nondestructive measurement of photon numbers in an optical cavity. The heart of the experiment consists in a single trapped calcium ion in the cavity. We drive the cavity with a very weak laser field to populate the cavity at the few photons level. The quantum state of the cavity photons are imprinted to the ions electronic state via a non-resonant interaction. The information of the photon numbers is extracted without destroying the photons. The state of the ion is measured with a high- resolution spectroscopy, and the corresponding spectrum is analyzed with a maximum likelihood method to reconstruct the photon numbers. The reconstruction works for the vacuum, coherent, and thermal-coherent states very well. In the optical domain, this experiment is the first demonstration of the intracavity field measurement and constitutes an important step to generate nonclassical states in a cavity. We expect that the obtained result is considered as a remarkable progress in the perspective of not only fundamental science but also applied aspects. In the research field of quantum optics, this experiment has the significance as a first demonstration of the intracavity field in the optical domain. This measurement employs a non-resonant interaction between the single atom and photons, which consists of a key ingredient to generate nonclassical cavity states like Fock states or Schrödinger cat states. In the microwave domain, a plethora of beautiful experiments has been reported using the interaction. Based on the achievement here, we believe that it now becomes possible to carry out such experiments in the optical domain. In the scope of recent quantum technology, the experiment can be regarded as a development of a new quantum sensor, in which a quantum system is used to measure physical properties that are inaccessible with any classical device. We demonstrated a nondestructive readout of the cavity photon numbers using the quantum coherence of the ion. This is simply not possible at all with any classical instruments. Such photon number resolving technique can find various applications in the research field of quantum metrology and quantum networks, like quantifying the sensitivity of a metrological device or testing a secure quantum communication protocol.