jackson-datatype-jsr310 を使う

Java 
<dependency>
    <groupId>com.fasterxml.jackson.datatype</groupId>
    <artifactId>jackson-datatype-jsr310</artifactId>
    <version>2.15.2</version>
</dependency>

SimpleModule を使う場合、

import com.fasterxml.jackson.databind.ObjectMapper;
import com.fasterxml.jackson.databind.module.SimpleModule;
import com.fasterxml.jackson.datatype.jsr310.deser.LocalDateTimeDeserializer;
import com.fasterxml.jackson.datatype.jsr310.ser.LocalDateTimeSerializer;

SimpleModule simpleModule = new SimpleModule();
simpleModule.addSerializer(LocalDateTime.class, new LocalDateTimeSerializer(DateTimeFormatter.ofPattern("yyyy/MM/dd HH:mm:ss")));
simpleModule.addDeserializer(LocalDateTime.class, new LocalDateTimeDeserializer(DateTimeFormatter.ofPattern("yyyy/MM/dd HH:mm:ss"))
ObjectMapper mapper = new ObjectMapper();
mapper.registerModule(simpleModule);

JavaTimeModule　は、SimpleModule の継承

import com.fasterxml.jackson.datatype.jsr310.JavaTimeModule;

JavaTimeModule jtm = new JavaTimeModule();
jtm.addSerializer(LocalDateTime.class, new LocalDateTimeSerializer(DateTimeFormatter.ofPattern("yyyy/MM/dd HH:mm:ss")));
jtm.addDeserializer(LocalDateTime.class, new LocalDateTimeDeserializer(DateTimeFormatter.ofPattern("yyyy/MM/dd HH:mm:ss"))
ObjectMapper mapper = new ObjectMapper();
mapper.registerModule(jtm);

JavaTimeModule は、内部で以下がシリアライザ、デシリアライザが登録されている。
ことから、こちらを使った方が良いかも。。。

// // Instant variants:
addDeserializer(Instant.class, InstantDeserializer.INSTANT);
addDeserializer(OffsetDateTime.class, InstantDeserializer.OFFSET_DATE_TIME);
addDeserializer(ZonedDateTime.class, InstantDeserializer.ZONED_DATE_TIME);

// // Other deserializers
addDeserializer(Duration.class, DurationDeserializer.INSTANCE);
addDeserializer(LocalDateTime.class, LocalDateTimeDeserializer.INSTANCE);
addDeserializer(LocalDate.class, LocalDateDeserializer.INSTANCE);
addDeserializer(LocalTime.class, LocalTimeDeserializer.INSTANCE);
addDeserializer(MonthDay.class, MonthDayDeserializer.INSTANCE);
addDeserializer(OffsetTime.class, OffsetTimeDeserializer.INSTANCE);
addDeserializer(Period.class, JSR310StringParsableDeserializer.PERIOD);
addDeserializer(Year.class, YearDeserializer.INSTANCE);
addDeserializer(YearMonth.class, YearMonthDeserializer.INSTANCE);
addDeserializer(ZoneId.class, JSR310StringParsableDeserializer.ZONE_ID);
addDeserializer(ZoneOffset.class, JSR310StringParsableDeserializer.ZONE_OFFSET);

// then serializers:
addSerializer(Duration.class, DurationSerializer.INSTANCE);
addSerializer(Instant.class, InstantSerializer.INSTANCE);
addSerializer(LocalDateTime.class, LocalDateTimeSerializer.INSTANCE);
addSerializer(LocalDate.class, LocalDateSerializer.INSTANCE);
addSerializer(LocalTime.class, LocalTimeSerializer.INSTANCE);
addSerializer(MonthDay.class, MonthDaySerializer.INSTANCE);
addSerializer(OffsetDateTime.class, OffsetDateTimeSerializer.INSTANCE);
addSerializer(OffsetTime.class, OffsetTimeSerializer.INSTANCE);
addSerializer(Period.class, new ToStringSerializer(Period.class));
addSerializer(Year.class, YearSerializer.INSTANCE);
addSerializer(YearMonth.class, YearMonthSerializer.INSTANCE);

/* 27-Jun-2015, tatu: This is the real difference from the old
 *  {@link JSR310Module}: default is to produce ISO-8601 compatible
 *  serialization with timezone offset only, not timezone id.
 *  But this is configurable.
 */
addSerializer(ZonedDateTime.class, ZonedDateTimeSerializer.INSTANCE);

// since 2.11: need to override Type Id handling
// (actual concrete type is `ZoneRegion`, but that's not visible)
addSerializer(ZoneId.class, new ZoneIdSerializer());
addSerializer(ZoneOffset.class, new ToStringSerializer(ZoneOffset.class));

// key serializers
addKeySerializer(ZonedDateTime.class, ZonedDateTimeKeySerializer.INSTANCE);

// key deserializers
addKeyDeserializer(Duration.class, DurationKeyDeserializer.INSTANCE);
addKeyDeserializer(Instant.class, InstantKeyDeserializer.INSTANCE);
addKeyDeserializer(LocalDateTime.class, LocalDateTimeKeyDeserializer.INSTANCE);
addKeyDeserializer(LocalDate.class, LocalDateKeyDeserializer.INSTANCE);
addKeyDeserializer(LocalTime.class, LocalTimeKeyDeserializer.INSTANCE);
addKeyDeserializer(MonthDay.class, MonthDayKeyDeserializer.INSTANCE);
addKeyDeserializer(OffsetDateTime.class, OffsetDateTimeKeyDeserializer.INSTANCE);
addKeyDeserializer(OffsetTime.class, OffsetTimeKeyDeserializer.INSTANCE);
addKeyDeserializer(Period.class, PeriodKeyDeserializer.INSTANCE);
addKeyDeserializer(Year.class, YearKeyDeserializer.INSTANCE);
addKeyDeserializer(YearMonth.class, YearMonthKeyDeserializer.INSTANCE);
addKeyDeserializer(ZonedDateTime.class, ZonedDateTimeKeyDeserializer.INSTANCE);
addKeyDeserializer(ZoneId.class, ZoneIdKeyDeserializer.INSTANCE);
addKeyDeserializer(ZoneOffset.class, ZoneOffsetKeyDeserializer.INSTANCE);